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AMERICAN  SCIENCE  SERIES,  ELEMENTARY  COURSE 


ELEMENTARY  ASTRONOMY 


BEGINNER'S   TEXT-BOOK 


BY 


EDWARD  S.  HOLDEN,  M.A.,  Sc.D.,  LL.D. 

Sometime  Director  of  the  Lick  Observatory 


NEW   YORK 

HENRY   HOLT  AND  COMPANY 
1899 


Copyright,  1899, 

BY 

HENRY  HOLT  &  CO. 


ROBERT    DRUMMOND.    PKINTER,  NHW    YORK. 


INTRODUCTION. 

THE  first  notions  of  Astronomy  are  acquired  in  the 
study  of  Geography.  Geography  lays  special  stress  on  the 
fact  that  the  surface  of  the  Earth  is  in  a  state  of  constant 
change.  Its  oceans  and  its  atmosphere  are  subject  to 
tides  ;  its  surface  is  leveled  for  the  sites  of  cities  and 
towns  ;  its  mines  and  quarries  are  explored  for  substances 
useful  to  mankind.  Men  navigate  its  seas  and  use  its  soils 
to  produce  the  food  that  supports  them.  Its  ceaseless 
changes,  natural  and  artificial,  give  to  it  a  kind  of  life — 
for  the  sign  of  life  is  change. 

Geography  teaches,  also,  that  the  Earth  is  one  of  the 
planets,  but  in  this  larger  relation  says  little  or  nothing  of 
changes  taking  place  in  the  solar  system.  The  youcg 
student  is  very  apt  to  conclude  that  the  other  planets  of 
whose  existence  he  knows — Venus  and  Jupiter  for  ex- 
ample— are  changeless,  immutable;  that  they  are  bright 
points  of  light  without  a  history.  This  was  the  view  of 
the  ancients. 

The  special  business  of  Astronomy  is  to  develop  the  ideas 
of  the  student  so  that  he  may  understand  that  all  the 
bodies  of  the  Solar  system — the  Sun  and  all  the  planets — 
are  themselves  subject  to  ceaseless  changes  and  are  thus 
endowed  with  a  kind  of  life.  Not  only  this;  the  bodies 
throughout  the  whole  universe — Sun  and  stars  alike — are 
perpetually  altering  both  their  places  and  the  arrangement 
of  their  separate  parts.  Our  life  on  the  Earth,  for  instance, 
would  quickly  cease  were  it  not  for  changes  in  the  Sun. 
There  are  many  stellar  systems  in  which  such  changes  have 

iii 

701040 


iv  INTRODUCTION. 

already  ceased  and  which  are  themselves  now  dead  as  the 
Moon  is  dead.  Others  again  are  in  their  prime  of  youth, 
and  still  others  are  in  their  ripe  maturity.  The  Cosmos  is, 
as  it  were,  alive;  and  it  is  still  in  a  state  of  uncompleted 
development. 

The  study  of  Astronomy  should  lead  the  student  to  com- 
prehensive ideas  of  the  universe  at  large.  He  will  gradually 
become  possessed  of  at  least  a  part  of  the  vast  body  of  re- 
sults that  has  been  slowly  amassed,  and,  what  is  even  more 
important,  of  the  methods  that  have  been  invented  by  the 
great  men  of  past  times  for  the  discovery  of  results.  A 
part  of  the  lesson  of  the  science  will  have  been  missed  if  it 
does  not  teach  a  sympathetic  admiration  for  great  names 
like  those  of  Galileo,  Kepler,  and  Newton.  Its  history  is 
intimately  connected  with  the  history  of  the  intellectual 
development  of  mankind. 

As  Astronomy  is  one  of  the  oldest  of  the  sciences  its 
methods  have  been  perfected  to  a  very  high  degree,  and 
have  served  as  models  for  the  methods  of  the  other  sciences. 
It  is  chiefly  for  this  reason  that  it  is  so  well  fitted  to  be  the 
science  first  studied  by  the  young  student. 

In  teaching  Astronomy  every  endeavor  should  be  made 
to  have  the  student  realize  what  he  learns.  What  is  al- 
ready known  about  the  Earth  will  serve  as  a  stepping-stone 
to  a  knowledge  of  the  planets.  When  something  is  learned 
of  the  planets,  the  knowledge  will  throw  light  upon  the 
past  (or  the  future)  condition  of  the  earth.  Jupiter  rep- 
resents, in  many  respects,  the  past  condition  of  the  Earth, 
just  as  the  Moon,  in  all  likelihood,  represents  its  state  in  a 
very  remote  future.  The  Sun  is  like  the  bright  stars 
strewn  by  thousands  over  the  celestial  vault — not  unlike 
them.  Everything  that  can  be  learned  regarding  the  Sun 
helps  us  to  comprehend  physical  conditions  in  the  stars, 
therefore;  and  the  converse  is  true. 

The  nebulae  are  not  exceptional  bodies  of  unique  nature, 


INTRODUCTION.  V 

but  they  are  examples  of  what  our  own  solar  system 
was  iii  ages  long  past.  Though  we  cannot  see  any  indi- 
vidual nebula  pass  through  all  the  stages  of  its  life  from  its 
birth  to  its  maturity,  we  can  select  from  the  vast  numbers 
of  such  bodies  particular  nebulas  in  each  especial  stage.  As 
Sir  William  Herschel  wrote  in  1789,  "This  method  of 
viewing  the  heavens  seems  to  throw  them  into  a  new  kind 
of  light.  They  are  now  seen  to  resemble  a  luxuriant  gar- 
den which  contains  the  greatest  variety  of  productions  in 
different  flourishing  beds;  and  we  can,  as  it  were,  extend  the 
range  of  our  experience  to  an  immense  duration.  For  is  it 
not  the  same  thing  whether  we  live  to  witness  successively 
the  germination,  blooming,  foliage,  fecundity,  fading, 
withering,  and  corruption  of  a  plant,  or  whether  a  vast 
number  of  specimens  selected  from  every  stage  through 
which  the  plant  passes  in  the  course  of  its  existence  be 
brought  at  once  to  our  view  ?  " 

It  should  be  the  aim  of  the  text-book  and  of  the  teacher 
to  so  marshal  the  most  significant  of  the  results  of  observa- 
tion that  the  student  may  acquire  such  wide  and  general 
views.  If  he  at  the  same  time  gains  a  luminous  idea  of 
the  most  important  of  the  methods  by  which  such  results 
are  reached,  his  teaching  has  been  successful.  It  is  neces- 
sary to  recollect,  on  the  other  hand,  that  it  is  not  the 
province  of  an  elementary  text-book  to  present  all  the 
latest  interpretations  of  observation,  or  to  give  more  than 
the  principles  of  the  methods  employed.  Details  of  the 
sort  cannot  be  thoroughly  understood  by  the  beginner. 
Questions  that  are  still  in  debate,  like  the  nature  of  the 
planet  Mars  or  the  constitution  of  comets,  cannot  be  pre- 
sented with  fulness  because  the  student  is  not  yet  sufficiently 
equipped  to  judge  the  points  at  issue.  At  the  same  time 
the  materials  for  such  a  judgment  should  be,  so  far  as 
possible,  laid  before  him  in  such  a  way  as  to  stimulate  his 
thought  and  his  imagination. 


vi  INTRODUCTION. 

In  all  the  natural  sciences  one  of  the  very  first  matters 
is  to  make  an  orderly  inventory  of  the  visible  universe. 
Things  must  then  be  grouped  into  classes,  in  order  that 
the  relations  of  the  various  classes  may  afterwards  be 
studied.  In  Astronomy  the  classes  are  few;  there  are  the 
Sun  and  the  stars,  the  planets,  the  comets,  the  nebulae. 
The  next  step  is  to  study  typical  members  of  each  class 
with  the  telescope.  All  that  the  text-book  can  do  is  to 
give  descriptions  of  the  appearances  presented  by  tele- 
scopes. These  must,  in  most  cases,  be  taken  on  faith. 

The  Moon  can  be  studied  to  advantage  by  opera-glasses 
or  by  such  small  telescopes  as  are  available  for  use  in 
schools.  Something  can  be  learned,  by  like  means,  of  the 
spots  on  the  Sun,  etc.  The  existence  of  the  brighter 
satellites  of  Jupiter  and  of  Saturn  can  be  verified.  But  for 
all  the  more  significant  facts  the  pupil  must  accept  the 
verbal  descriptions  of  the  book.  The  apparent  motions  of 
the  stars  and  planets  can  perfectly  well  be  observed,  out  of 
doors,  by  the  student  who  has  time  and  opportunity.  But 
here  again  there  are  difficulties.  Dwellers  in  city  streets, 
seldom  have  an  uninterrupted  view  of  the  sky;  and  even 
those  who  live  in  the  country  rarely  have  time  enough  to 
give  to  actual  observation.  It  is  entirely  impossible  in  a 
few  weeks  to  even  verify  what  it  has  taken  centuries  to 
disclose. 

All  the  actual  observing  of  the  heavens  that  can  be  ar- 
ranged for  should  be  done.  Its  chief  use  will  be  to  illus- 
trate by  actual  examples  the  methods  laid  down  in  the 
text-book.  Conviction  will  come  to  the  pupil  because  he 
has  learned  hoiv  to  prove  or  to  disprove  its  theorems;  not 
because  he  has  actually  made  the  proofs  for  himself.  He 
knows  that  if  he  has  sufficient  time  they  can  be  proved  or 
disproved  by  following  a  certain  method.  He  thoroughly 
understands  the  method  and  he  has  applied  it  in  a  few 
cases.  He  is  satisfied  that  the  method  itself  is  adequate 


INTRODUCTION.  vii 

and  he  accepts  the  conclusions — even  those  that  he  has  not 
himself  tested.  If  the  student  will  take  the  time  and  the 
pains  to  actually  make  the  observations  suggested,  he  will 
learn  much.  Enough  is  here  given  to  start  him  on  his 
way  and  to  make  it  easy  for  him  to  go  on  by  himself. 

The  present  book  endeavors  to  place  the  pupil  in  this 
independent  position  by  suggesting  tests  that  he  can  him- 
self apply.  Quite  as  much  stress  is  laid  on  the  spirit  of  the 
methods  of  the  science  as  on  the  results  to  which  those 
methods  have  led.  And  the  separate  results  of  observation 
are  prized  mainly  because  each  one  bears  on  an  explanation 
of  the  whole  universe.  . 

This  book  is  condensed  from  two  volumes  previously 
written  by  Professor  SIMOIST  NEWCOMB  and  myself  for  the 
American  Science  Series.  I  have  to  express  my  sincere 
thanks  to  him  for  permission  to  print  the  condensation  in 
its  present  form,  and  to  the  Astronomical  Society  of  the 
Pacific,  to  Professor  CHARLES  A.  YOUNG,  and  to  Dr.  J,  E. 
KEELEE,  Director  of  the  Lick  Observatory,  for  permission 
to  use  some  of  the  cuts  here  printed. 

The  book  is  addressed  especially  to  pupils  who  are  study- 
ing Astronomy  for  the  first  time.  The  chief  difficulties  of 
such  students  are  not  due  to  the  intrinsic  complexity  of  the 
separate  problems  that  they  meet,  but  rather  to  their  appar- 
ent want  of  connection  one  with  another,  and  above  all  to  the 
unfamiliarity  01  the  student  with  the  methods  of  reasoning 
employed.  It  is  therefore  necessary  to  treat  each  new  topic 
with  great  clearness,  and  not  to  dismiss  it  until  its  relation 
to  other  topics  has  been  at  least  partially  apprehended. 
The  important  point  is  to  present  the  subject  in  a  way  to 
convince  and  to  enlighten  the  pupil,  and  this  object  can 
only  be  attained  in  a  text-book  by  some  repetitions  and  by 
avoiding  undue  brevity.  This  volume  contains  more 
pages  than  one  of  its  predecessors  in  the  American  Science 
Series.  The  increased  space  is  given  to  very  full  explana- 


viii  INTRODUCTION. 

tions  of  difficult  points,  to  lists  of  test-questions,  and  to 
pictures  and  diagrams.  Where  the  mathematical  equip- 
ment of  the  pupil  is  not  yet  adequate — as  in  the  case  of 
NEWTON'S  discoveries  in  Celestial  Mechanics,  for  example — 
an  historical  treatment  must  be  adopted. 

It  is  probable  that  most  of  the  students  who  will  read 
this  book  will  not  pursue  the  subject  further  in  the  way  of 
formal  studies.  Their  ideas  of  the  measurement  of  time, 
of  the  apparent  and  real  motions  of  the  planets,  of 
the  cause  of  the  seasons,  and  of  other  fundamental  and 
practical  matters  of  the  sort,  will  be  derived  from  this  one 
course  of  study.  Especial  stress  is  therefore  laid  on  such 
topics,  and  many  interesting  subjects  of  less  importance  are 
passed  by  with  a  mere  mention,  or  are  omitted  altogether. 
The  prescribed  limits  of  space  do  not  permit  a  treatment 
of.  all  the  parts  of  a  vast  science  like  Astronomy. 

It  may  sometimes  be  useful  to  the  teacher,  and  it  will 
always  be  so  to  the  student,  to  refer  to  the  questions  printed 
in  Part  I,  which  will  suggest  new  ways  of  testing  the 
knowledge  gained  by  the  reading  of  each  lesson.  It  is  not 
here  attempted  to  set  down  all,  or  any  great  part,  of  the 
questions  which  each  topic  may  suggest,  but  only  to  give 
such  as  are  most  essential  and  important. 

If  the  student  finds  that  he  has  an  answer  in  clear  and 
definite  English  for  each  of  the  questions  given  here,  he 
may  be  sure  that  he  has  comprehended  the  explanations  of 
the  text.  And  he  should  not  finally  leave  any  topic  until 
he  does  so. 

The  second  part  of  the  book  is  mainly  devoted  to  a  de- 
scription of  the  bodies  of  the  solar  system,  one  by  one,  and 
to  some  account  of  nebulae,  stars,  and  comets.  It  is  to  be 
expected  that  the  formal  studies  of  the  pupil  will  have 
created  a  living  interest  in  such  information,  and  that  he 
will,  for  his  own  pleasure,  read  some  of  the  many  admira- 
ble popular  works  on  Astronomy  that  we  owe  to  Mr.  PROG- 


INTRODUCTION.  IX 

TOR,  Sir  EOBEKT  BALL,  and  others.  The  text-book  will 
have  performed  its  part  if  such  an  interest  has  been  awak- 
ened, and  if  at  the  same  time  a  solid  foundation  for  the 
student's  future  reading  has  been  laid.  For  this  reason 
Parts  II  and  III  of  this  book  have  been  somewhat  ab- 
breviated. 

If  the  class  has  sufficient  time  it  is  desirable  that  the 
teacher  should  supplement  his  instruction  by  reading,  with 
the  students,  certain  chapters  from  the  books  of  the 
school  library  named  in  Chapter  XXIX.  Chapters  bearing 
on  a  certain  subject  can  be  selected  by  the  teacher  from 
the  books  referred  to,  after  the  students  have  studied  the 
corresponding  chapter  in  the  present  volume.  If  such 
books  cannot  be  had  articles  from  encyclopaedias  will  serve 
in  their  stead. 

It  will  not  be  out  of  place  to  give  a  few  practical  hints 
based  on  experience.  Excellent  training  in  observation 
can  be  had  from  tracing  the  areas  and  the  boundaries  of 
the  constellations.  The  positions  of  the  brighter  stars  of 
each  constellation  should  first  be  fixed  in  the  memory. 
There  are  ten  stars  of  the  first  magnitude  and  about  thirty 
of  the  second  magnitude  in  the  northern  sky.  After  these, 
or  most  of  them,  have  been  identified,  the  constellation 
figures  may  be  taken  up  one  by  one  and  their  boundaries 
traced.  The  six  small  star-maps  of  this  book  can  be 
used  for  this  purpose  in  connection  with  the  Map  of  the 
Equatorial  Stars.  A  celestial  globe  is  even  more  con- 
venient and  satisfactory,  and  every  school  should  own  one 
if  it  is  practicable.  It  should  be  constantly  used  to  illus- 
trate or  to  prove  the  theorems  of  the  text-book. 

The  globe  will  be  a  material  aid  in  planning  any 
series  of  observations,  and  it  should  be  always  at  hand  to 
explain  the  results  of  observations  already  made. 

The  course  of  one  of  the  bright  planets  among  the  stars 


x  INTRODUCTION. 

should  be  mapped  from  night  to  night.  The  path  of  the 
Moon,  also,  should  be  followed  whenever  it  is  practicable. 
The  place  of  a  planet  can  be  fixed  with  considerable  pre- 
cision by  noting  its  allineations  with  two  or  more  stars.  In 
these  observations  it  will  be  found  useful  to  employ  a 
straight  ruler  three  or  four  feet  long.  The  phases  of  the 
Moon  can  be  studied  with  the  eye,  or  better,  with  a  com- 
mon opera-glass.  A  watch  regulated  to  sidereal  time 
should  form  a  part  of  the  equipment  of  the  school. 

If  a  small  telescope  on  a  firm  stand  is  available  much 
may  be  done  by  its  aid.  Many  of  the  surface-features  of 
the  bright  planets  (Mars,  Jupiter)  can  be  made  out.  The 
existence  of  the  larger  satellites  of  Jupiter  and  Saturn  can 
be  proved.  The  ring  of  Saturn  can  be  seen.  Some  of  the 
double  stars  can  be  separated.  The  brighter  nebulas  can 
be  shown.  Some  of  the  principal  star  groups  or  clusters 
can  be  studied.  The  changes  in  brightness  of  a  short- 
period  variable  star  can  be  observed.  The  spots  on  the 
Sun  can  be  shown  by  projecting  the  Sun's  image  on  a 
screen. 

In  these  observations  it  is  important  to  do  the  work 
thoroughly  and  systematically.  If  the  satellites  of  Jupiter 
are  in  the  field  every  student  in  the  class  should  see  all  of 
the  bright  satellites  that  are  then  visible.  If  a  double  star 
is  viewed  it  should  be  looked  at  until  both  its  components 
are  plainly  seen,  and  so  with  other  cases.  No  one  should 
leave  the  telescope  unconvinced.  The  object  of  such 
observations  is  to  make  an  ocular  demonstration  of  facts 
that  have  heretofore  been  received  on  faith,  not  to  make 
additions  to  science.  For  this  reason  the  instructor  should 
select  the  objects  to  be  examined,  with  care.  They  should 
be  typical,  but  not  difficult  to  make  out.  Each  student 
should  be  required  to  keep  neat,  accurate,  and  concise 
notes  of  his  own  observations,  and  whenever  a  drawing  or 
a  diagram  will  explain  the  observation  he  should  be 


INTRODUCTION.  xi 

required  to  make  it.  All  observations  should  be  dated  and 
authenticated  with  the  pupil's  signature.  He  should  be 
taught  to  feel  a  responsibility  for  the  records  that  he 
makes. 

The  student  should  be  practised  in  pointing  out  in  the 
sky  the  principal  lines  and  points  of  the  celestial  sphere — 
the  meridian,  the  equator,  the  ecliptic,  the  vernal  equinox, 
the  poles  of  the  two  last-named  circles,  and  so  forth.  There 
is  no  mystery  in  these  plain  geometric  figures.  A  little 
practice  will  serve  to  make  them  quite  familiar. 

The  school  should  own  a  small  collection  of  works  on 
popular  and  descriptive  astronomy,  which  can  be  loaned 
to  the  students  for  reading  at  home.  These  can  be  selected 
by  the  teacher  and  added  to  the  equipment  of  the  school 
from  time  to  time,  as  fast  as  circumstances  permit. 
Simple  models  to  illustrate  the  motions  of  the  different 
instruments  of  astronomy  are  easy  to  make,  and  they  are  of 
great  practical  utility  in  the  class-room.  Most  of  them 
can  be  made  by  the  pupils.  If  practicable,  models  of  the 
sextant,  the  transit  instrument,  the  meridian  circle  and  the 
equatorial  should  be  provided.  Directions  for  making 
such  models  are  given  in  the  text. 

Finally  it  is  of  the  first  importance  that  difficulties 
should  not  be  shirked.  To  be  useful,  the  student's  work 
should  be  thorough  so  far  as  it  goes.  An  instructor  (or  a 
writer  of  text-books)  is  often  tempted  to  smooth  away  ob- 
stacles, forgetting  that  one  great  use  of  the  study  of 
science  is  to  train  the  mind  to  resolutely  meet  and  to  con- 
quer difficulties.  The  advantage  of  scientific  problems  is 
that  they  are  capable  of  a  definite  solution,  and  that  the 
student  himself  cannot  fail  to  know  whether  he  has  or  has 
not  accomplished  that  which  he  set  out  to  do.  If  our 
nation  is  to  take  and  hold  a  foremost  place  in  the  world, 
it  will  do  so  through  the  predominance  of  certain  qualities 


xii  INTRODUCTION. 

in  its  citizens  that  scientific  education  can  foster  to  a  very 
important  degree.  We  cannot  afford  to  neglect  any  means 
of  developing  thoroughness  and  faithfulness  in  the  per- 
formance of  duty  in  those  who  will  soon  be  the  responsible 
governors  of  our  country.  E.  S.  H. 

NEW  YORK,  June  17,  1899. 


TABLE  OF  CONTENTS. 

(Consult  the  index  at  the  end  of  the  book  also.) 
PART  I.— INTRODUCTION. 

CHAPTER  PAGE 

I.  INTRODUCTORY — HISTORICAL 1 

II.  SPACE— THE  CELESTIAL  SPHERE— DEFINITIONS 15 

III.  DIURNAL  MOTION  OF  THE  SUN,  MOON,  AND  STARS..  41 

IV.  THE  DIURNAL  MOTION  TO  OBSERVERS  IN  DIFFER- 

ENT LATITUDES,  ETC 59 

V.  CO-ORDINATES — SIDEREAL  AND  SOLAR  TIME 77 

VI.  TIME — LONGITUDE 94 

VII.  ASTRONOMICAL  INSTRUMENTS . ... 112 

VIII.  APPARENT  MOTION  OF  THE  SUN  TO  AN  OBSERVER 

ON  THE  EARTH — THE  SEASONS 154 

IX.  THE  APPARENT  AND  REAL  MOTIONS  OF  THE  PLAN- 
ETS— KEPLER'S  LAWS 179 

X.  UNIVERSAL  GRAVITATION 203 

XI.  THE  MOTIONS  AND  PHASES  OF  THE  MOON 216 

XII.  ECLIPSES  OF  THE  SUN  AND  MOON  222 

XIII.  THE  EARTH 232 

XIV.  CELESTIAL  MEASUREMENTS  OF  MASS  AND  DISTANCE.  260 

PART   II.— THE   SOLAR   SYSTEM. 

XV.  THE  SOLAR  SYSTEM 269 

XVI.  THE  SUN 280 

XVII.  THE  PLANETS  MERCURY,  VENUS,  MARS 299 

xiii 


xiv  TABLE  OF  CONTENTS.       , 

CHAPTER  PAGE 

XVI11.  THE  MOON— THE  MINOR  PLANETS 315 

XIX.  THE    PLANETS    JUPITER,     SATURN,     URANUS,    AND 

NEPTUNE 325 

XX.  METEORS 347 

XXI.  COMETS 357 

PART  III.— THE  UNIVERSE  AT  LARGE. 

XXII.  INTRODUCTION 369 

XXIII.  MOTIONS  AND  DISTANCES  OF  THE  STARS. 379 

XXIV.  VARIABLE  AND  TEMPORARY  STARS 386 

XXV.  DOUBLE,  MULTIPLE,  AND  BINARY  STARS 390 

XXVI.  NEBULAE  AND  CLUSTERS , 393 

XXVII.  SPECTRA  OF  FIXED  STARS 400 

XXVIII.  COSMOGONY 407 

XXIX.  PRACTICAL  HINTS  ON  MAKING  OBSERVATIONS— LISTS 
OF  INTERESTING  CELESTIAL  OBJECTS— MAPS  OF 
THE  STARS 414 

APPENDIX — SPECTRUM  ANALYSIS 433 

INDEX.  .  .  441 


SYMBOLS  AND  ABBREVIATIONS. 


SIGNS   OF   THE   PLANETS,    ETC. 


© 


9  or 


The  San. 
The  Moon. 
Mercury. 
Venus. 
The  Earth. 


Mars. 

Jupiter. 

Saturn. 

Uranus. 

Neptune. 


The  asteroids  are  distinguished  by  a  circle  enclosing  a  number, 
which  number  indicates  the  order  of  "discovery,  or  by  their  names,  or 
by  both,  as  (TOO) ;  Hecate. 

The  Greek  alphabet  is  here  inserted  to  aid  those  who  are  not 
already  familiar  with  it  in  reading  the  parts  of  the  text  in  which  its 
letters  occur : 

Names. 
Alpha 
Beta 
Gamma 


Letters. 
A   a 
B  ft 

r  y 

A  8 
E  e 


Delta 

Epsilon 

Z  C  Zeta 

77  77  Eta 

0  §  0  Theta 

/  i  Iota 

K  K  Kappa 

A  A  Lambda 

M  ju  Mu 

THE   METRIC    SYSTEM. 

MEASURES    OF    LENGTH. 

1  kilometre    =  1000  metres        =    0.62137  mile. 
1  metre  =  the  unit  =  39.370  inches. 

1  millimetre  =  W^  of  a  metre  =    0  03937  Inch. 


Letters. 

Names. 

N  r 

Nu 

(3  £ 

Xi 

0    0 

Omicron 

n  it  it 

Pi 

P  p 

Rho 

2  a  S 

Sigma 

T  r 

Tau 

r  v 

Upsilon 

<p  <p 

Phi 

xx 

Chi 

w  •$ 

Psi 

fi    GO 

Omega 

MEASURES   OF   WEIGHT. 

1  kilogramme  =  1000  grammes  =    2.2046  pounds. 
1  gramme          =  the  unit  =  15.432  grains. 

Tbe  following  rough  approximations  may  be  memorized  : 

The  kilometre  is  a  little  more  than  ^  of  a  mile,  but  less  tlian  f  of 
a  mile.     The  mile  is  \fa  kilometres. 

The  kilogramme  is  2i  pounds.     The  pound  is  less  than  half  a  kilo- 
gramme. 

One  metre  is  3.3  feet.     One  metre  is  39.4  inches. 

xv 


ASTRONOMY. 


CHAPTER   I. 

INTRODUCTORY— HISTORICAL. 

1.  Astronomy  defined. — Astronomy  (from  the  Greek 
,  a  star,  and  rojtos,  a  law)  is  the  science  that  is  con- 
cerned about  the  laws  that  the  heavenly  bodies  obey,  and 
wi  th  a  description  of  the  bodies  themselves  both  as  they  ap- 
pear to  be  and  as  they  really  are.  For  instance  the  Sun  ap- 
pears to  us  very  different  from  a  bright  star;  but  astron- 
omy shows  that  the  Sun  is  itself  a  star  like  thousands  of 
others  that  we  see  in  the  sky  at  night.  The  Sun  appears  to 
move  across  the  sky  from  east  to  west,  from  rising  to  set- 
ting, every  day.  Astronomy  explains  that  this  motion  is 
only  apparent  and  that,  in  fact,  it  is  caused  by  the 
Earth's  turning  on  its  axis,  daily. 

The  Sun  appears  to  move  among  the  stars  so  as  to  go 
completely  around  the  sky  from  one  star  back  to  the  same 
star  again  every  year.  Astronomy  proves  that,  in  fact, 
the  Sun  does  not  move,  but  that  its  apparent  course  is 
nothing  but  the  result  of  the  Earth's  real  motion  around 
an  orbit — a  path — with  the  Sun  near  its  centre.  The 
planets,  like  the  stars,  appear  to  shine  by  their  own  light. 

1 


&:  ASTRONOMY. 

Astronomy  shows  that  the  planets  shine  by  reflected  sun- 
light, while  the  light  of  the  stars  is  native  to  them.  As- 
tronomy is  the  science  that  seeks  the  true  explanation  of 
the  appearances  presented  by  the  stars.  Astronomy  is  the 
science  of  the  stars;  or  more  particularly,  it  is  the  science 
that  explains  what  the  stars  really  are,  how  they  really 
move,  and  why  they  appear  to  move  as  they  do.  The 
word  star  is  used  so  as  to  include  planets,  comets,  the 
Sun,  the  Moon,  etc.  It  is  used  as  the  Greeks  used  it,  to 
mean  any  heavenly  body. 

2.  How  we  get  our  notions  of  the  Universe  of  Stars. — We 
know  things  on  the  Earth  through  our  senses,  by  touching 
them,  tasting,  smelling,  hearing,  or  seeing  them.  A  piece 
of  iron  can  be  felt  and  weighed  as  well  as  seen.  If  one 
of  our  senses  makes  a  mistake,  another  sense  often  comes 
in  to  correct  the  error.  A  piece  of  cork  might  be  painted 
so  as  to  look  precisely  like  a  piece  of  iron  of  the  same  size. 
The  sight  alone  could  not  distinguish  between  them.  But 
if  we  take  the  two  things  in  our  hands,  the  sense  of  touch 
or  of  weight  detects  a  difference  at  once. 

Stars  in  the  sky  are  known  to  us  only  through  the  sense 
of  sight.  If  that  sense  is  deceived,  there  is  no  other  one 
to  correct  it.  A  blind  person  can  know  much  about  things 
on  the  Earth,  but  he  can  know  very  little  indeed  about 
the  stars  that  he  cannot  see.  All  our  first-hand  notions  of 
the  universe  of  stars  come  to  us  through  our  sense  of  sight. 

Our  eyes  tell  us  how  things  appear  to  be,  and  we  do  not 
know  how  they  really  are  until  we  have  reasoned  about  the 
appearances  and  sifted  out  the  truth.  A  bright  rainbow 
looks  almost  like  a  solid  arch  in  the  sky,  while  it  is,  in 
fact,  not  in  the  sky  at  all.  It  is  in  our  own  eyes.  When 
we  travel  in  a  railway  train,  parts  of  the  landscape  seem 
to  be  moving  about  other  parts  ;  yet  nothing  is  more  cer- 
tain than  that  the  landscape  is  really  unchanged.  It  re- 
quires reasoning  to  interpret  such  appearances. 


INTROD  UCTOR  T— HISTORICAL.  3 

—  What  senses  can  you  use  to  learn  about  things  on  the  Earth  ? 
Give  an  example  of  a  thing  that  you  can  touch  ?  of  a  thing  that  you 
can  taste  ?  of  a  thing  that  you  can  hear  ?  From  all  these  separate 
senses  you  gain  notions  of  things  on  the  Earth.  How  do  you  get  your 
ideas  about  a  star  ?  It  is  by  the  sense  of  sight  alone,  is  it  not  ?  If 
you  have  only  one  sense  to  help  you,  you  have  to  be  extremely  care- 
ful not  to  be  deceived  by  it.  Give  some  examples  of  how  the  sense 
of  sight  deceives  in  appearances  on  the  Earth. 

3.  The  Heavens  were  carefully  observed  by  the  An- 
cients.— The  very  first  man  could  not  fail  to  notice  the 
rising  and  setting  of  the  Sun.  The  coming  of  Night — 
often  a  time  of  terror  and  danger  to  him — was  a  mystery  ; 
and  the  advent  of  successive  days  was  a  perpetual  miracle. 
The  Sun  brought  cheerfulness,  safety,  warmth,  comfort. 
His  rays  made  plants  grow  and  provided  food.  He  was 
worshipped  as  a  God  by  the  men  of  early  times.  When 
the  Sun  was  darkened  by  an  eclipse  and  the  day  itself  grew 
black  the  people  were  filled  with  dread.  Special  men — 
priests — were  appointed  to  observe  such  occurrences  and 
to  foretell  them.  It  was  by  the  diligent  watching  of  these 
priests  that  the  different  appearances  in  the  sky  were  first 
carefully  noted,  and  the  first  lists  of  the  stars  made. 

By  and  by,  as  men  in  general  had  more  leisure,  the 
science  of  the  stars,  like  other  sciences,  was  studied  for  its 
own  sake.  Men  were  curious  to  understand  why  the  Sun 
rose  and  set;  why  it  was  sometimes  eclipsed,  and  so  forth. 
Moreover,  their  knowledge  of  astronomy  was  put  to  prac- 
tical uses.  In  the  earliest  times  navigators  did  not  dare  to 
venture  out  of  sight  of  land,  or  to  make  voyages  at  night. 
They  sailed  from  headland  to  headland  during  the  day,  and 
tied  their  little  vessels  to  the  shore  at  night.  They  steered 
their  course  by  landmarks.  But  wise  men  had  noticed 
that  while  the  stars  in  general  rose  and  set,  there  were 
some  stars  that  were  always  visible — the  North  Star,  for 
example.  They  could  use  the  North  Star  for  a  steering- 
mark  by  night,  then ;  and  so  they  did. 


4  ASTRONOMY. 

Nearly  three  thousand  years  ago  (1012  B.C.)  SOLOMON 
built  the  Temple  at  Jerusalem  and  ornamented  it  with  gold 
brought  by  ships  from  South  Africa.  The  Phoenicians 
(who  lived  on  the  north  shores  of  Africa)  brought  tin 
from  England  about  the  same  time.  These  long  voyages 
must  have  been  made  by  using  the  stars  as  guides  by  night. 


FIG.  1. — THE  STARS  OF  THE  NORTHERN  SKY. 

The  Pole-star  is  at  the  centre  of  the  cut.  The  Great  Bear  (the  Dipper)  is 
at  the  left-hand  side.  The  arrows  show  the  direction  in  which  the  stars 
move  round  the  pole. 

The  mariner's  compass,  which  is  our  guide  nowadays,  was 
not  known  in  Europe  before  A.D.  1300,  though  the  Chi- 
nese sailors  used  it  long  before  that  time. 


IN  TROD  UCTOR  T-HISTORICAL.  5 

—  What  was  the  earliest  observation  of  astronomy?  Who  were 
the  first  astronomers?  After  the  priests,  who  studied  the  stars? 
How  did  astronomy  make  itself  useful  to  navigation  ?  What  star  is 
always  visible  on  clear  nights  in  our  part  of  the  world  ?  Does  the 
North  Star  rise  and  set  ?  Mention  some  long  voyages  made  by  the 
ancients. 

4.  Some  of  the  great  astronomers  of  ancient  times. 

We  do  not  know  the  names  of  the  ancient  priests  and 
wise  men  of  Assyria,  Babylon,  China,  and  Egypt  who  first 
studied  the  stars.  A  few  of  their  records  that  have  come 
down  to  us  date  back  to  2200  B.C.  in  Chaldaea  and  to  2900 
B.C.  in  China.  Our  history  of  astronomy  begins  long 
after  their  time,  with  the  Greeks,  about  six  centuries  be- 
fore Christ,  about  2500  years  ago.  The  Greeks  of  that  time 
were  a  very  intelligent,  clever,  hardy,  adventurous  people, 
eager  to  learn  and  to  practice  what  they  learned.  They 
were  good  sailors  and  good  soldiers. 

THALES  (pronounced  tha'lez),  one  of  the  seven  wise  men 
of  Greece,  was  born  about  640  B.C.  He  showed  his  coun- 
trymen how  to  divide  the  year  into  seasons.  At  midsum-  \^\^ 
mer  the  Sun  at  noon  was  higher  in  the  heavens  than  at  any 
other  time  of  the  year  (about  June  21).  At  midwinter 
the  Sun,  at  noon,  was  lowest  (about  December  22).  These 
were  the  two  solstices  (pronounced  sol'sti-ces).  About 
March  20  and  September  22  the  days  and  nights  were  of 
equal  length  (at  the  two  ejcpjnoxes).  March  20  was  the 
vernal,  or  spring,  equinox;  September  22  was  the  autum- 
nal equinox.  Each  and  every  year  could  be  divided  into 
seasons  in  this  way  because  the  Sun  was  always  highest  in 
the  heavens  (nearest  to  the  point  overhead)  in  June,  al- 
ways lowest  in  December  ;  because  the  days  and  nights 
were  always  of  equal  length  in  March  and  in  September. 
THALES  did  not  know  why  this  was  so.  But  he  knew  the 
facts.  And  he  first  showed  the  Greeks  how  to  divide  their 
year  into  parts.  Before  his  time  the  Greek  sailors  had 


6  ASTRONOMY. 

steered  their  ships  by  the  stars  of  the  Great  Bear  (see  Fig. 
1).  He  showed  them,  it  is  said,  that  the  stars  of  the 
Little  Bear,  which  were  nearer  the  pole,  would  serve  the 
purpose  better. 

ANAX'IMANDER,  a  friend  of  THALES  (610  B.C.)  invented 
the  sun-dial.  The  shadow  of  an  upright  column  made  by 
the  Sun  moved  during  the  day,  and  the  motion  of  the 
shadow  marked  the  passing  of  the  hours.  Sun-dials  were 
the  first  clocks.  He  explained  why  it  is  that  the  Moon 
changes  every  month  from  a  crescent  (new  Moon)  to  a 
full  Moon ;  and  other  matters. 

PYTHAG'ORAS  (born  582  B.C.)  travelled  in  Egypt  and 
learned  much  of  the  science  of  the  Egyptian  priests.  Sev- 
eral of  the  Egyptian  pyramids  were  built  at  least  a  thou- 
sand years  before  Christ,  and  many  of  them  were  built  by 
astronomical  rules,  so  as  to  face  the  North  Star  and  so 
forth.  PYTHAGORAS  brought  much  foreign  science  home 
to  the  Greeks.  It  was  he  who  first  taught  his  countrymen 
that  the  morning  and  the  evening  star  ( Venus)  was  the 
same  body.  It  had  formerly  been  thought  that  Phos- 
phorus (the  name  for  the  morning  star)  and  Hesperus  (the 
evening  star)  were  two  different  planets.  It  was  a  great 
discovery  to  learn  that  there  was  only  one  planet,  some- 
times seen  in  the  west  at  sunset,  sometimes  in  the  east 
about  sunrise.  You  know  the  fact,  just  as  PYTHAGORAS 
did  twenty-four  centuries  ago.  He  did  not  thoroughly 
understand  why  it  was  so,  but  the  reason  will  be  plain  to 
you  before  you  have  finished  this  little  book. 

ANAXAG'ORAS  (born  500  B.C.)  knew  all  the  bright  plan- 
ets— Mercury,  Venus,  Mars,  Jupiter,  and  Saturn — and 
understood  how  they  moved  in  the  heavens,  among  the 
stars.  He  knew  that  the  stars  did  not  move  among  each 
other.  A  group  of  stars  like  the  Great  Dipper  (see  Fig. 
1)  keeps  the  same  shape  during  centuries.  Planets  (wan- 
dering stars)  move  among  the  fixed  stars.  ANAXAGORAS 


INTROD  UCTORY— HISTORICAL.  7 

explained  eclipses  too.  He  said  that  the  dark  body  of  the 
Moon  came  in  between  the  Sun  and  the  Earth  and  shut  off 
the  Sun's  light,  just  as  your  hand  held  in  front  of  a  candle 
shuts  off  its  light. 

AR'ISTOTLE  (born  384  B.C.)  was  the  first  Greek  to  prove 
that  the  Earth  is  a  globe.  He  was  the  friend  of  ALEXAN- 
DER the  Great  and  the  pupil  of  PLATO,  who  was  the  pupil 
of  SOCRATES.  He  studied  every  kind  of  science  and  wrote 
many  books.  (Books  in  his  day  were  manuscripts  of 
course  ;  printing  was  not  invented  in  Europe  till  about 
A.D.  1450,  though  the  Chinese  had  practiced  the  art  long 
before.)  ALEXANDER  the  Great  founded  a  splendid  city 
— Alexandria,  in  Egypt — and  endowed  it  with  schools,  col- 
leges, libraries,  museums,  observatories.  It  was  full  of 
learned  men  of  all  sorts  :  physicians,  geographers,  gram- 
marians, mathematicians,  and  among  them  were  many 
famous  astronomers.  EUCLID,  the  geometer,  was  born 
there  about  300  B.C.  ;  ARCHIME'DES,  the  famous  mathe- 
matician (born  287  B.C.),  studied  there  ;  ERATOS'THENES 
(born  276  B.C.)  was  the  keeper  of  the  Royal  Library,  and 
there  he  made  a  great  map  of  the  world  and  tried  to 
measure  the  circumference  of  the  earth. 

HIPPARCHUS  (born  160  B.C.)  was  an  Alexandrian,  too, 
and  he  is  the  Father  of  Astronomy.  He  collected  all  the 
observations  of  the  men  who  had  gone  before  him  and 
made  great  discoveries  of  his  own,  of  which  we  shall  hear 
more.  Most  of  his  writings  are  lost,  but  his  discoveries 
are  described  by  PTOLEMY  of  Alexandria  (who  lived  in  the 
first  century  after  Christ)  in  his  great  work  the  Almagest. 
This  book,  which  sums  up  all  the  astronomical  knowledge 
of  the  ancients,  was  the  greatest  scientific  work  of  the  Old 
World.  Its  doctrines  were  believed  and  taught  in  all  the 
schools  and  universities  of  Europe  from  PTOLEMY'S  time 
up  to  the  time  of  GALILEO  (died  1642) — that  is,  for  fifteen 
centuries. 


8  ASTRONOMY. 

PTOLEMY'S  book  declared  that  the  Earth  was  the  centre 
of  the  Universe,  and  that  the  Sun  and  all  the  planets  moved 
round  it.  Another  great  book  was  written  by  COPERKICUS 
(died  1543)  to  prove  that  the  Sun  and  not  the  Earth  was 
the  centre  of  the  system ;  and  that  the  Earth  was  only  one 
of  the  planets,  all  of  which  moved  round  the  Sun.  This 
was  and  is  the  truth ;  but  it  was  not  established  until  the 
discoveries  made  by  GALILEO  (1610)  with  the  telescope 
that  he  constructed. 

Still  another  great  book,  the  Principia,  was  written  by 
Sir  ISAAC  NEWTON  in  1687,  to  prove  that  all  the  motions 
of  all  the  planets  and  all  the  stars  are  the  results  of  one 
single  force — the  force  of  gravitation  or  attraction  exerted 
by  every  heavy  body  on  every  other  such  body.  NEW- 
TON is  the  Father  of  Modern  Astronomy,  just  as  HIP- 
PARCHUS  was  the  Father  of  the  Astronomy  of  the  Ancients. 
The  books  of  PTOLEMY,  of  COPERNICUS,  and  of  NEWTON 
are  landmarks  in  the  history  of  Astronomy.  Their  dates 
should  be  remembered:  A.D.  140,  A.D.  1543,  A.D.  1687. 

—  When  does  the  history  of  astronomy  begin?  To  what  nation 
did  the  first  learned  astronomers  belong?  What  sort  of  a  people 
were  the  Greeks  ?  Who  showed  the  Greeks  how  to  divide  the  year 
into  seasons  ?  When  did  THALES  live  ?  Who  invented  the  sun- 
dial ?  Who  first  explained  the  changes  in  the  Moon's  shape  ? 
When  did  ANAXIMANDER  live?  What  Greek  brought  home  the 
learning  of  the  Egyptians?  When  did  PYTHAGORAS  live?  Who 
first  taught  how  the  planets  moved  among  the  stars  ?  and  that  the 
stars  were  fixed  ?  and  explained  eclipses  ?  About  what  time  did 
ANAXAGORAS  live  ?  When  did  ARISTOTLE  live  ?  He  was  the  friend 
of  what  great  King?  Who  founded  Alexandria  in  Egypt?  What 
sorts  of  learning  were  encouraged  there  ?  Name  some  of  the  famous 
men  who  studied  and  taught  there.  Who  is  called  the  Father  of 
Astronomy  ?  What  is  the  name  of  PTOLEMY'S  great  book  ?  How 
long  was  the  Almagest  the  greatest  authority  on  astronomy  ?  Where 
was  the  centre  of  the  Universe  acording  to  PTOLEMY  ?  Where  did 
COPERNICUS  (1543)  place  it  ?  Whose  discoveries  proved  COPERNI- 
CUS to  be  right  ?  Who  constructed  the  first  telescope  ?  When  did 


INTRODUCTORY— HISTORICAL.  9 

GALILEO  live  ?  Who  is  the  Father  of  Modern  Astronomy  ?  When 
was  the  Principia  of  Sir  ISAAC  NEWTON  written? 

5.  How  Astronomy  might  be  studied. 

In  the  paragraphs  just  preceding,  a  few  of  the  names  of  the  great 
men  of  past  times  have  been  mentioned  and  something  has  been  said 
of  their  discoveries.  If  there  were  time  enough  there  could  be  no 
better  way  to  study  Astronomy  than  to  follow  its  history  step  by  step 
from  the  most  ancient  times  until  now.  Six  centuries  before  Christ, 
2500  years  ago,  the  earliest  Greek  philosophers  began  to  study 
science  for  its  own  sake.  They  were  curious  about  the  world  around 
them  and  about  all  the  appearances  they  saw  in  the  sky.  They 
wished  to  understand  the  motions  of  the  planets,  their  distances,  the 
shape  and  size  of  the  Earth,  the  cause  of  eclipses,  and  so  on.  One 
after  another  of  their  great  men  accurately  described  or  fully  ex- 
plained motions  or  appearances  in  the  sky. 

Each  philosopher  taught  what  he  had  learned  to  his  favorite 
pupils  by  word  of  mouth.  They  in  their  turn  taught  others  in  the 
same  way.  Finally  in  the  time  of  Alexander  the  Great  (332  B.C.) 
the  city  of  Alexandria  in  Egypt  was  founded,  and  splendidly  en- 
dowed with  colleges,  schools,  museums,  observatories,  and  so  forth. 
Learned  men  were  invited  thither  from  every  other  city.  For  sev- 
eral centuries  it  was  the  centre  of  learning  for  the  whole  world.  Its 
libraries  contained  700,000  manuscripts.  Here  a  succession  of  great 
astronomers  and  mathematicians  laid  the  foundations  of  the  science. 
The  work  of  HIPPARCHUS  was  gathered  together  in  a  systematic 
treatise  (the  Almagest]  by  PTOLEMY,  and  this  book  held  its  place  of 
authority  for  fifteen  centuries. 

Alexandria  was  conquered  by  Rome  in  30  B.C.  When  the  Roman 
Empire  was  rained  in  the  IV  century  the  fortunes  of  the  city  de- 
clined, and  it  was  itself  captured  and  sacked  by  the  Saracens  in  641 
A.D.  Learning,  especially  scientific  learning,  was  at  a  very  low  ebb 
in  Europe  during  the  Dark  Ages  (A.D.  400  to  1400).  It  was  not 
until  the  time  of  COLUMBUS  (1492)  and  COPERNICUS  (1543)  that  ad- 
vances were  made,  except  by  the  Moors  in  Spain  (709  A.D.  to  1492). 
The  universities  and  schools  established  in  these  centuries  still 
taught  the  astronomy  of  ARISTOTLE  and  of  PTOLEMY. 

The  great  book  of  COPERNICUS  (De  OrUum  ccelestmm  revolutioni- 
bus — on  the  revolutions  of  the  celestial  bodies)  was  printed  in  1543. 
It  announced  and  proved  the  great  discovery  that  the  Sun  and  not 
the  Earth  was  the  centre  of  the  celestial  motions.  The  doctrine  of 
PTOLEMY  declared  that  the  Sun  and  planets  moved  around  the 
Earth.  GALILEO  constructed  the  first  astronomical  telescope  in  1 609, 


10  ASTRONOMY. 

and  in  1610  be  made  such  discoveries  by  its  aid  tbat  tbe  Copernican 
doctrine  was  fully  established  in  the  minds  of  all  competent  judges. 
But  there  were  few  such  judges  in  his  day. 

KEPLER  discovered  the  laws  according  to  which  the  planets  move 
in  their  orbits  in  the  years  1609-1618.  But  it  was  not  until  tbe  ap- 
pearance of  Sir  ISAAC  NEWTON'S  Principia  in  1687 — a  little  more 
than  two  centuries  ago — that  modern  astronomy  was  born.  He  an- 
nounced and  proved  that  all  the  motions  and  all  the  appearances  in 
the  Universe  were  mere  consequences  of  a  single  law  of  gravitation, 
of  attraction.  Since  his  time  immense  advances  have  been  made,  but 
most  of  them  are  but  consequences  of  his  law,  and  are  explained  by  it. 
Astronomical  instruments  have  been  wonderfully  improved  also,  and 
great  discoveries  have  been  made.  The  system  of  COPERNICUS,  as 
explained  by  NEWTON,  has  been  firmly  established  by  all  these  ad- 
vances. 

If  there  were  leisure  to  follow  out  in  detail  all  these  discoveries 
and  advances,  the  pupil  could  be  taken  through  the  experience  of 
the  race  and  could  successively  master  each  great  problem  just  as  it 
was  mastered  by  THALES,  HIPPARCHUS,  COPERNICUS,  and  NEWTON. 
There  is  no  more  satisfactory  and  thorough  method  of  study  than 
this.  Unfortunately  it  requires  far  more  time  than  is  available.  It 
is  impossible,  here,  to  explain  the  system  of  the  world  according  to 
PTOLEMY  and  to  take  the  time  to  prove  it  to  be  wrong.  All  that  can 
be  done  is  to  explain  the  system  of  COPERNICUS  and  to  prove  it  to  be 
right.  It  is  necessary,  therefore,  to  study  Astronomy  in  our  High 
Schools  in  a  different  order.  Each  subject  must  be  so  treated  as  to 
prepare  the  way  for  other  topics,  and  everything  must  be  presented 
in  the  briefest  manner.  The  science  of  Astronomy  is  so  vast,  and  so 
many  brilliant  discoveries  have  been  made  by  so  many  able  men,  that 
the  limits  of  this  little  book  do  not  permit  an  historical  treatment. 

—  How  long  ago  were  the  beginnings  of  the  Astronomy  of  the 
Greeks?  How  did  the  ancient  Greek  philosophers  teach  their  pupils? 
When  was  the  city  of  Alexandria  founded  ?  How  many  manuscripts 
were  contained  in  its  libraries?  (The  National  Library  at  Washing- 
ton has  not  even  now  so  many  books.)  Ask  your  teacher  to  tell  you 
about  the  Dark  Ages  in  Europe,  or  else  read  about  them  in  an  en- 
cyclopaedia. What  system  of  Astronomy  was  taught  in  European 
universities  in  those  times  ?  Where  did  PTOLEMY  say  the  centre  of 
the  universe  was  ?  COPERNICUS  (1543)  taught  that  the  centre  of  the 
world  was — where?  Which  is  right ?  It  will  be  abundantly  shown 
in  this  book  that  COPERNICUS  was  right. 


INTROD  UGTOR  T— HISTORICAL.  1 1 

6.  General  notions  of  Astronomy. 

Even  before  beginning  the  study  of  Astronomy  every 
one  of  us  has  a  certain  knowledge  of  it.  All  of  us  have 
studied  Geography  and  know  what  is  there  said  of  the  Sun 
and  planets;  all  of  us  have  heard  certain  facts  of  Astron- 
omy talked  about ;  and  every  one  of  us  has  observed  a  few 
things  for  himself.  Let  us  set  down  something  like  an  in- 
ventory of  this  general  knowledge  here.  It  is  well  to  find 
out  just  what  we  know  now  before  going  on  to  new  things. 

The  Earth  is  a  huge  globe,  so  large  that  any  small  part  of  it,  where 
we  live,  looks  flat  and  not  round.  Its  diameter  is  nearly  8000  miles. 
We  know  that  the  Earth  is  a  globe  because  it  was  circumnavigated 
by  MAGELLAN'S  ships  in  the  years  1519-1522,  and  by  hundreds  of 
vessels  since  that  time  ;  and  because  nearly  every  part  of  it  has  been 
visited  by  travellers  ;  and  finally  because  surveys  have  been  made  of 
most  civilized  countries.  The  Earth  is  certainly  a  globe  ;  and  its  size 
is  enormous  compared  to  our  houses,  cities,  etc.  It  is  not  large  com- 
pared  to  the  Sun  and  to  some  of  the  other  planets.  It  is  isolated  in 
space.  It  does  not  touch  any  other  planet  or  star.  Even  the  Moon 
is  very  distant  from  it,  and  the  Sun  is  much  further  away.  The  stars 
are  further  off  still. 

The  Earth  turns  round  on  its  axis  once  in  every  day,  and  its  turn- 
ing makes  the  Sun  and  the  Moon  and  the  stars  appear  to  rise  and  set. 
Moreover  the  Earth,  like  the  other  planets,  moves  round  the  sun  in 
an  orbit — a  path — once  in  a  year,  and  this  revolution  of  the  Earth 
has  something  to  do  with  the  seasons — Spring,  Summer,  Autumn, 
Winter — which  recur  regularly  every  year. 

The  Sun  looks  to  us  like  a  large  flat  disc,  but  it  is,  in  fact,  a  huge 
globe,  much  larger  than  the  Earth.  It  is  the  source  from  which 
comes  all  our  light  and  all  our  heat.  Our  seasons — Spring,  Summer, 
Autumn,  and  Winter — depend  upon  the  amount  of  heat  received  from 
the  Sun  at  different  times.  Just  what  makes  the  light  and  heat  we 
do  not  learn  from  Geography,  and  that  is  one  of  the  important  things 
taught  in  our  text-books  of  Physics.  All  the  planets — the  Earth, 
Venus,  Jupiter,  etc.,  move  round  the  Sun  in  orbits — paths — and  to- 
gether make  up  the  Solar  System — the  Family  of  the  Sun. 

The  Moon  also  looks  to  us  like  a  flat  disc,  but  it  is,  in  fact,  a  globe, 
smaller  than  the  Earth.  It  revolves  about  the  Earth,  not  about  the 


12  ASTRONOMY. 

Sun,  in  an  orbit — path,  and  it  is  very  far  away  from  us.  Sometimes 
its  shape  is  that  of  a  crescent ;  sometimes  it  is  circular.  It  regularly 
goes  through  all  its  shapes  and  comes  back  to  the  same  shape  again 
once  in  every  month,  and  so  on  forever.  The  Moon  sometimes  comes 
between  the  Earth  and  the  Sun  and  shuts  off  some  or  all  of  the  Sun's 
light  in  the  daytime  and  makes  an  eclipse,  just  as  a  book  held  in 
front  of  a  candle  will  cut  off  the  candlelight  and  eclipse  it.  The 
Moon  is  usually  bright,  but  it  is  itself  sometimes  eclipsed.  The  face 
of  the  Moou  seen  by  the  naked  eye  at  night  (o-r  seen  through  an 
opera-glass  or  a  telescope)  is  not  everywhere  the  same.  Parts  of  it 
are  much  brighter  than  other  parts  ;  and  there  are  mountains  on  the 
Moon. 

-The  Planets  look  to  us  like  bright  stars.  Venus  is  often  seen  to- 
wards the  west  at  sunset,  and  is  called  the  Evening  Star  ;  and  some- 
times we  may  have  seen  it  towards  the  east  about  sunrise,  when  it  is 
called  the  Morning  Star.  It  is  brighter  than  most  of  the  stars. 
Jupiter,  Mars,  and  Saturn  are  planets  that  look  like  stars,  too. 

The  Comets  are  sometimes  very  bright,  we  have  heard.  They 
move  about  in  space,  and  people  say  that  if  one  should  hit  the  Earth 
there  would  be  a  great  disaster.* 

The  Stars  lie  all  around  us,  and  they  are  visible  by  hundreds  at 
night.  Most  of  them  rise  and  set,  but  there  are  some  near  the  North 
Pole  that  are  always  visible  whenever  it  is  night.  They  are 
divided  into  constellations,  or  groups  ;  and  one  of  the  groups  is  called 
the  Great  Bear  or  the  Dipper.  Some  of  the  stars  are  quite  bright, 
others  much  fainter.  If  a  telescope  is  used,  many  thousands  of  stars 
can  be  seen  that  are  invisible  to  the  naked  eye.  The  stars  are  ex- 
ceedingly far  away  from  us. 

If  some  one  who  had  not  yet  studied  Astronomy  were 
asked  to  give  his  notions  about  the  heavenly  bodies  he 
would  prohably  say  something  like  what  has  been  printed 
in  the  preceding  paragraphs.  The  information  is  generally 
correct  so  far  as  it  goes,  but  there  are  many  things  lacking 
to  make  it  complete.  We  ought  to  know  wliy  it  is  that 
the  seasons  come  back  to  us  year  after  year  in  order;  why 

*  It  may  as  well  be  said  here  that  in  the  first  place  such  a  collision 
is  very  unlikely  to  happen  ;  and  that  if  it  did  happen  it  is  probable 
that  the  Earth  would  not  suffer. 


INTROD  UCTOR  Y— HISTORICAL.  1 3 

the  Son  gives  ns  light  and  heat  ;  why  the  Sun  is  eclipsed 
by  the  Moon  sometimes,  and  why  ifc  is  not  eclipsed  every 
month;  why  the  Moon  itself  is  sometimes  eclipsed,  and  so 
forth.  Perhaps  the  most  important  thing  that  is  left  out 
of  this  account  is  the  fact  that  the  Sun  shines  hy  its  own 
light  (just  as  an  electric  light  does),  while  the  Moon  and 
all  the  planets  do  not  shine  by  their  own  light,  but  by  re- 
flected sunlight.  They  appear  bright  just  as  a  mirror  that 
is  shined  upon  appears  bright.  If  you  shut  off  the  light, 
the  mirror  is  no  longer  bright.  If  the  Sun  were  to  be  an- 
nihilated, all  the  planets  and  the  Moon  would  instantly  be 
dark.  They  are  only  bright  because  the  sunlight  shines 
upon  them  and  because  they  reflect  the  sunlight  back  to  the 
Earth  much  as  a  mirror  might  do.  All  the  stars  are  suns, 
and  each  and  every  star  shines  by  its  own  light,  just  as  the 
Sun  does. 

With  these  additional  facts  about  the  Sun,  which  shines 
by  its  own  light;  about  the  planets,  which  shine  by  reflect- 
ed light;  and  about  the  stars,  which  shine,  like  the  Sun,  by 
native  light,  we  can  go  on  to  study  Astronomy  in  detail. 
We  have  a  general  idea  of  it  to  begin  with,  and  we  know 
some,  at  least,  of  the  lacks  in  our  present  knowledge. 
This  book  does  not  take  such  general  knowledge  to  be 
proved.  On  the  other  hand  the  facts  above  set  down  will 
be  explained  and  proved.  But  as  every  one  has  some 
knowledge  of  astronomical  facts,  the  book  is  not  written  as 
if  no  one  had  any  information  of  the  kind. 

—  How  do  we  know  that  the  Earth  is  a  globe  ?  Who  first  circum- 
navigated it  ?  How  long  ago  ?  How  do  we  know  that  the  Earth  is 
isolated  in  space  ?  Two  of  the  Earth's  motions  make  the  day  and  the 
year — which  two?  What  heavenly  body  that  you  know  of  goes 
through  a  series  of  changes  every  month  ?  Does  the  Sun  shine  by  his 
own  light?  Does  the  Moon  shine  by  her  own  light?  Do  the  planets 
so  shine  ?  If  you  could  stand  a  long  way  off  from  the  Earth,  would 


14:  ASTRONOMY. 

the  Earth  be  dark  or  would  it  sbine  like  the  other  planets  ?  Do  the 
stars  shine  by  the  light  of  the  Sun  ?  Suppose  the  Sun  suddenly  be- 
came dark  so  that  it  gave  out  no  more  light,  what  changes  would 
this  make  in  the  appearance  of  the  sky  at  night  ?  What  bodies 
would  no  longer  be  visible  ?  What  others  would  continue  to  shine 
unchanged  ? 


CHAPTER  II. 
SPACE— THE  CELESTIAL  SPHERE— DEFINITIONS. 

7.  Space. — The  Sun,  the  planets,  and  all  the  stars  are 
moving  in  Space.  It  is  often  called  "  empty  "  Space  be- 
cause it  contains  no  large  masses  except  the  Sun  and  plan- 
ets, the  stars,  the  comets,  and  so  forth.  It  is  necessary  to 
have  some  idea  of  its  vastness,  for  it  contains  all  these 
bodies  and  every  other  thing  that  exists.  It  is  infinite — 
without  any  limits  or  boundaries.  For  suppose  it  had  a 
boundary,  what  would  lie  beyond  that  ?  Only  more  and 
further  extensions  of  space.  We  cannot  realize  exactly  or 
even  imagine  what  Space  is;  but  we  can  obtain  a  few  cor- 
rect ideas  about  it. 

Suppose  that  on  a  clear  night  you  look  up  at  the  full 
Moon  in  the  heavens.  It  seems  to  be,  and  it  is,  extremely 
distant.  It  is  240,000  miles  away.  It  is  240  times  as  dis- 
tant from  us  as  New  York  is  from  Chicago.  Now  think  of 
the  Sun,  which  is  870,000  miles  in  diameter.  The  diam- 
eter of  the  globe  of  the  Sun  is  about  3£  times  the  distance 
of  the  Moon  from  the  Earth.  The  Sun  is  one  of  the  stars, 
and  there  are  hundreds  and  hundreds  of  bright  stars  visi- 
ble to  the  naked  eye.  There  are  millions  and  millions  of 
stars  visible  in  a  great  telescope.  All  these  stars  are  scat- 
tered about  in  space  somewhat  as  pictured  on  page  16. 

Space  contains  millions  of  stars,  and  each  star  (as  «,  #, 
c,  etc.)  is  at  least  as  far  from  every  other  star  (as/,  g,  li,  i, 
ky  Z,  m,  etc.)  as  the  nearest  stars  (Z>,  c,  #,  h,  I,  m)  are 
from  the  Sun. 

15 


16  ASTRONOMY. 

Try  to  conceive  this  arrangement  of  stars  clearly.  They 
are  scattered  everywhere  in  Space.  There  are  millions 
upon  millions  of  them.  Each  one  of  them  is  as  distant 
from  its  nearest  neighbor  as  the  stars  nearest  to  the  Sun  are 
distant  from  the  Sun.  Now  how  far  is  the  nearest  star 
from  the  Sun?  We  shall  see  by  and  by  that  it  is  at  least 
20,000,000,000,000  miles;  that  is,  twenty  millions  of  mil- 
lions of  miles.  Every  other  star  in  the  sky  is  as  distant 
from  its  nearest  neighbor  as  this.  And  there  are  millions 
of  such  stars  in  succession  one  to  another  as  we  go  out- 


*  *  3 

/  g  Sun 


lc  I  in  n  o 

FIG.  2. 

The  stars  are  arranged  in  Space  somewhat  as  in  the  picture,  only  not  in 
a  plane,  but  throughout  a  solid. 


wards  through  Space.  Space  contains  them  all,  and  there 
is  room  for  countless  millions  more.  The  spaces  between 
them  are  empty. 

Let  us  try  to  realize  this  in  another  way.  Think  first 
of  the  Sun — it  is  870,000  miles  in  diameter.  Then  think 
of  the  nearest  star.  It  is  20,000,000,000,000  miles  from 
the  Sun.  Then  imagine  a  whole  universe  of  countless 
millions  of  stars  no  one  nearer  to  another  than  twenty 
billion  miles.  All  these  stars  may  be  thought  of  as  a 
great  cluster  in  the  shape  of  a  globe.  Imagine  this  cluster 
to  shrink  and  shrink,  to  get  smaller  and  smaller.  The 
stars  will  come  nearer  and  nearer  to  each  other,  and  the 
globe  of  the  Sun  (870,000  miles  in  diameter,  remember) 


SPACE- THE  CELESTIAL  SPHERE— DEFINITIONS.    17 

will  also  grow  smaller  at  the  same  time  and  in  the  same 
proportion.  Let  the  shrinking  go  on  till  the  universe  is 
2,300,000,000  times  smaller  than  at  first — till  the  Sun's 
globe  is  only  two  feet  in  diameter,*  and  then  stop  the 
shrinking. 

We  shall  have  a  model  of  the  universe  with  everything 
in  its  true  proportions,  only  the  Sun  will  be  two  feet 
in  diameter  instead  of  870,000  miles.  Now  how  far 
off  will  the  nearest  star  to  the  Sun  be,  in  this  shrunken 
model  of  the  universe?  It  will  be  as  far  from  the  San  as 
the  city  of  Peking  is  from  the  city  of  New  York  !  The 
nearest  star  will  be  so  far  off.  The  other  stars  will  be  ar- 
ranged in  order  out  beyond  this  one,  and  none  of  them 
will  be  any  nearer,  in  this  model,  to  its  neighbors  than  the 
distance  from  China  to  New  York.  And  the  model  mus~t 
contain  millions  of  stars.  Even  this  model  will  be  incon- 
ceivably large.  The  real  universes-Space — is  inconceiva- 
bly larger  than  the  model.  An.  illustration  like  this  en- 
tirely fails  to  give  a  measure  of  the  size  of  Space,  but  it 
certainly  does  give  some  conception  of  its  immense  exten- 
sion. In  thinking  of  the  universe  of  stars  you  must  try 
to  realize  it  in  this  way.  The  Sun  and  all  the  stars  lie  in 
space,  none  of  them  near  together,  with  immense  empty 
regions  between  the  different  bodies.  Each  star  is  incon- 
ceivably far  from  its  nearest  neighbors,  and  there  are  mil- 
lions upon  millions  of  stars.  It  is  not  at  all  easy  to  have 
clear  ideas  of  an  infinite  extension  ;  but  it  is  absolutely 
necessary  in  beginning  the  study  of  Astronomy  to  have 
some  idea  of  the  space  in  which  the  Sun,  all  the  planets, 
and  all  the  stars  exist. 

—  Why  do  we  call  Space  "empty"?  How  far  away  is  the  Moon 
from  the  Earth  ?  The  diameter  of  the  globe  of  the  Sun  is  how  much 
larger  than  this  distance  ?  Is  the  Sun  a  star  ?  Space  contains  mil- 


*  Two  feet  is  OTnrtsffTnnnjtk  part  of  870,000  miles. 


18  ASTRONOMY. 

lions  upon  millions  of  stars.  Each  star  is  at  least  twenty  millions  of 
millions  of  miles  from  its  nearest  neighbors.  Are  the  spaces  be- 
tween them  empty  of  large  bodies?  Suppose  you  could  make  an 
exact  model  of  Space  with  each  star  in  its  right  place,  and  suppose 
you  could  make  this  model  shrink  until  the  870,000  miles  of  the 
Sun's  diameter  had  shrunk  to  two  feet — how  far  off  would  the  star 
nearest  to  the  Sun  be  from  the  Sun  itself  ?  Would  these  words  do 
for  a  definition  of  Space — Space  is  indefinite  extension  ?  If  you  have 
a  dictionary,  look  up  the  word  and  see  how  it  is  defined  there. 

8.  The  Celestial  Sphere. — In  what  has  just  heen  said 
about  Space  we  have  spoken  of  the  universe  as  it  really  is. 
The  stars  are  scattered  all  about  through  Space  at  enormous 
distances  one  from  another.  That  is  the  way  the  universe 
really  is.  Now  we  have  to  ask  how  does  it  appear  to  be  to 
us  ?  If  you  look  at  the  heavens  on  a  clear  night  what  do 
you  see  ?*  In  the  first  place  you  see  hundreds  of  stars,  some 
very  bright,  some  less  bright.  They  all  seem  to  be  at  the 
same  distance  from  you.  They  look  as  if  they  were  bright 
points  fastened  to  the  inside  surface  of  a  great  hollow  globe 
— the  celestial  sphere — hung  over  the  Earth.  You  see  the 
bright  points.  The  surface  on  which  you  imagine  them 
to  lie  is  called  the  celestial  sphere.  There  is,  in  fact,  no 
such  surface,  but  there  seems  to  be  one.  Let  us  make  a 
formal  definition  of  it  which  is  to  be  learned  by  heart. 
The  Celestial  Sphere  is  that  surface  to  which  the  stars  seem 
to  he  fastened.  No  one  ever  thinks  of  the  stars  as  if  they 
were  outside  of  the  celestial  sphere  and  shining  through  it. 

In  Fig.  3  the  black  square  is  a  part  of  Space.*  There 
are  a  few  stars  in  it,  namely  p,  q,  r,  s,  £,  £,  £,  u,  v.  In 
respect  to  the  immense  distances  of  the  stars,  the  Earth,  0, 
may  be  considered  as  a  mere  point.  The  configurations  of 
the  stars  are  the  same  whether  you  are  at  Lisbon  or  at 

*  The  student  must  remember  here  and  throughout  the  book  that 
the  drawings  have  to  be  on  a  small  scale.  All  the  Universe  has  to 
be  drawn  on  a  few  square  inches. 


SPACE— THE  CELESTIAL  SPHERE—  DEFINITIONS.   19 

New  York.  No  change  of  place  on  the  Earth  alters  the 
grouping  of  the  stars.  You  are  on  the  Earth  looking  out 
at  the  sky  at  night  and  you  see  all  these  stars.  If  you  look 
at  the  star  which  is  really  at  q  you  are  looking  along  the 
line  Oq  and  see  it  as  if  it  were  on  the  surface  of  the  celes- 
tial sphere  at  Q.  If  you  look  at  r  and  s,  you  see  them  at 


FIG.  '6. — THE  CELESTIAL  SPHERE. 

The  Earth  is  supposed  to  be  at  O,  a  few  of  the  stars  at  p,  q,  7%  s,  t,  t,  t,  w,  v. 
These  stars  are  seen  by  us  as  if  they  were  all  on  the  surface  of  the  celes- 
tial sphere  at  P,  Q,  R,  S,  T,  17,  V. 

R  and  S.  If  you  look  at  u  and  v  you  see  them  at  U  and 
V.  All  of  them  appear  to  be  at  one  and  the  same  distance 
from  you,  though  they  really  are  at  very  different  dis- 
tances. The  point  Q  is  in  the  line  Oq  prolonged;  the 
points  R,  8,  U,  V  are  in  the  lines  Or,  Os,  On,  Ov  pro- 
longed. Now  suppose  there  happened  to  be  three  stars,  t, 


20  ASTRONOMY. 

t,  t,  in  a  line.  They  would  all  three  appear  on  the  celes- 
tial sphere  at  T.  You  would  never  know  there  were  three 
separate  stars,  because  yon  could  only  see  one  bright  point 
— at  T.  You  do  not  see  the  other  stars  r,  s,  v,  etc., 
where  they  really  are,  but  at  places  on  the  celestial  sphere 
at  R,  8,  F. 


FIG>  4.— THE  EARTH  (n,  q,  *)  IN  THE  CENTRE  OF  THE  CELESTIAL 

SPHERE. 

On  the  surface  of  the  celestial  sphere  meridians  and  parallels  are  sup- 
posed to  be  drawn  corresponding  to  meridians  and  parallels  on  the  Earth. 


What  you  see  in  a  dark  night  is  stars  apparently  studded 
over  the  inner  surface  of  the  celestial  sphere.  It  is  only 
by  reasoning  about  it  that  you  know  they  are  not  on  this 
surface  but  scattered  about  inside  of  the  sphere.  The  an- 


SPACE— THE  CELESTIAL  SPHERE-DEFINITIONS.    21 

cient  astronomers  thought  that  the  sphere  actually  existed 
and  that  the  stars  were  really  fastened  to  it.  Although  it 
does  not  exist,  the  idea  can  be  made  to  serve  a  useful  pur- 
pose. For  instance,  if  we  want  to  know  the  angle  be- 
tween the  two  lines  Or  and  Os  (the  angle  between  the  two 
lines  joining  the  Earth  and  two  distant  stars)  all  we  have 
to  do  is  to  measure  the  arc  RS  on  the  celestial  sphere. 
The  arc  RS  is  the  measure  of  the  angle  rOs  in  space. 

The  sphere  has  other  uses,  too.  Just  as  there  is  a  ter- 
restrial equator  on  the  globe  of  the  Earth  (and  terrestrial 
meridians,  etc.),  so  there  is  a  celestial  equator  (and  celes- 
tial meridians,  etc.)  on  the  celestial  sphere.  The  simplest 
part  of  astronomy  deals  with  the  apparent  places  of  stars 
as  they  seem  to  be  on  the  celestial  sphere — it  is  called 
Spherical  Astronomy  for  that  reason.  It  is  only  after  we 
have  learned  about  the  apparent  places  and  motions  of 
stars  and  planets  that  we  can  go  on  to  study  their  real 
motions.  So  that  the  idea  of  a  celestial  sphere  will  be  use- 
fnl.  Whenever  you  go  out  at  night  you  will  see  it — it  is 
the  dark  sphere  on  which  the  bright  stars  seem  to  rest. 
Imagine  that  the  stars  are  not  there  ;  yet  the  sphere  will 
remain.  Every  one  imagines  the  blue  vault  of  the  sky  in 
the  daytime  as  if  it  were  a  hollow  sphere  hanging  over  us. 
The  Sun  seems  to  be  on  its  inner  surface.  When  you  see 
the  Moon  in  the  daytime  it,  too,  seems  to  lie  on  the  celes- 
tial sphere. 

—  The  stars  really  are  at  very  different  distances  from  us  ;  all  are 
very  far  away,  but  some  are  much  further  away  than  others — do 
they  seem  to  be  at  different  distances  when  you  look  at  them  at 
night  ?  Do  they  seem  to  lie  on  the  inner  surface  of  a  sphere  ?  What 
is  the  celestial  sphere  ?  Is  it  a  sphere  that  really  exists,  or  only  one 
that  appears  to  exist  ?  Does  the  celestial  sphere  seem  to  exist  in  the 
daytime  as  well  as  at  night? 

9.  Some  Mathematical  Terms  used  in  Astronomy. — It 


22  ASTRONOMY. 

is  convenient  to  use  a  few  mathematical  terms  in  speaking 
about  the  geometrical  parts  of  Astronomy.  All  of  the 
mathematical  ideas  here  introduced  are  simple,  but  it  may 
be  well  to  set  them  down  in  order.  If  they  are  under- 
stood by  the  student  he  will  have  no  difficulty  in  compre- 
hending the  astronomical  matters  that  are  to  be  spoken  of. 
If  they  are  not  thoroughly  understood  some  points  will  not 
be  as  clear  as  they  should  be. 

ANGLES:  THEIR  MEASUREMENT. — An  angle  is  the 
amount  of  divergence  of  two  lines.  For  example,  the 
angle  between  the  two  lines  S1E 
and  S*E  is  the  amount  of  diver- 
gence of  these  lines.  The  angle 
S*ES*  is  the  amount  of  divergence 
of  the  two  lines  S*E  and  S'E. 
The  eye  sees  at  once  that  the 
angle  S*ES*  in  the  figure  is 
greater  than  the  angle  /S'1^2, 

FIG.  5. -ANGLES:  THEIR     and     that     the     angle    S'W    is 
MEASUREMENT.  greater  than  either  of  them. 

In  order  to  compare  them  and  to  obtain  their  numerical  ratio,  we 
must  have  a  unit-angle. 

The  unit-angle  is  obtained  in  this  way  ;  The  circumference  of  any 
circle  is  divided  into  360  equal  parts.  The  points  of  division  are 
joined  with  the  centre.  The  angles  between  any  two  adjacent  radii 
are  called  degrees.  In  the  figure,  SES*  is  about  12°,  S*ES*  is  about 
22°,  S*ES*  is  about  30°,  and  &ES*  is  about  64°.  The  vertex  of  the 
angle  is  at  the  centre  E ;  the  measure  of  the  angle  is  on  the  circum- 
ference S]S*SSS*,  or  on  any  circumference  drawn  from  E  &s  a  centre. 

In  this  way  we  have  come  to  speak  of  the  length  of  one  three- 
hundred-and-sixtieth  part  of  any  circumference  as  a  degree,  because 
radii  drawn  from  the  ends  of  this  part  make  an  angle  of  1°. 

For  convenience  in  expressing  the  ratios  of  different  angles  the 
degree  has  been  subdivided  into  minutes  and  seconds. 

One  circumference  =  360°  =  21600'  =  1296000" 
1°  =    60'  =  360" 
V  =    60" 


SPACE-THE  CELESTIAL  SPHERE-DEFINITIONS.   23 

Smaller  angles  than  seconds  are  expressed  by  decimals  of  a  second. 
Thus  one-quarter  of  a  second  is  0".25;  one-quarter  of  a  minute 
is  15". 


The  Radius  of  the  Circle  in  Angular  Measure. — If  R  is 
the  radius  of  a  circle,  we  know  from  geometry  that  one 
circumference  =  2  nR,  where  n  =  3.1416.  That  is, 

2  nR  -   360°  =  21600'  =  1296000" 
or  R  =  57°.3  =  3437'.7  =  206264".8. 

By  this  we  mean  that  if  a  flexible  cord  equal  in  length 
to  the  radius  of  any  circle  were  laid  round  the  circumfer- 
ence of  that  circle,  and  if  two  radii  were  then  drawn  to  the 
ends  of  this  cord,  the  angle  of  these  radii  would  be  57°. 3, 
3437'.7,  or  206264".8. 

It  is  important  that  this  should  be  perfectly  clear  to  the 
student. 

For  instance,  how  far  off  must  you  place  a  foot-rule  in  order 
that  it  may  subtend  an  angle  of  1°  at  your  eye?  Why,  57.3  feet 
away.  How  far  must  it  be  in  order  to  subtend  an  angle  of  a  min- 
ute? 3437.7  feet.  How  far  for  a  second?  206264.8  feet,  or  over  39 
miles. 

Again,  if  an  object  subtends  an  angle  of  1°  at  the  eye,  we  know 

that  its  diameter  must  be  ==-5  as  great  as  its  distance  from  us.    If  it 
07.  o 

subtends  an  angle  of  1",  ita  distance  from  us  is  over  200,000  times  as 
great  as  its  diameter. 

The  instruments  employed  in  astronomy  may  be  used  to 
measure  the  angles  subtended  at  the  eye  by  the  diameters 
of  the  heavenly  bodies.  In  other  ways  we  can  determine 
their  distance  from  us  in  miles.  A  combination  of  these 
data  will  give  us  the  actual  dimensions  of  these  bodies  in 
miles.  For  example,  the  sun  is  about  93,000,000  miles 
from  the  Earth.  The  angle  subtended  by  the  sun's  diam- 


24  ASTRONOMY. 

eter  at  this  distance  is  1922".  What  is  the  diameter  of  the 
sun  in  miles?  (1"  is  about  451  miles.) 

An  idea  of  angular  dimensions  in  the  sky  may  be  had 
by  remembering  that  the  angular  diameters  of  the  Moon 
and  of  the  Sun  are  about  30'.  It  is  180°  from  the  west 
point  to  the  east  point  counting  through  the  point  immedi- 
ately overhead.  How  many  moons  placed  edge  to  edge 
would  it  take  to  reach  from  horizon  to  horizon?  The 
student  may  guess  at  the  answer  first  and  then  com- 
pute it. 

It  is  convenient  to  remember  that  the  angular  distance 
between  the  two  "Pointers"  in  the  Great  Bear  (see  Fig.  1) 
is  about  5°. 

PLANE  TRIANGLES. — The  angles  of  which  we  have  spoken  are 
angles  in  a  plane.  In  any  plane  triangle  there  are  three  angles  A,  B,  G 
and  three  sides  a,  b,  c — six  parts.  If  any  three  of  the  parts  are  given 
(except  the  three  angles)  we  can  construct  the  triangle.  For  in- 


FIG.  6.  —A  PLANE  FIG.  7. — Two  SIMILAR  PLANE 

TRIANGLE.  TRIANGLES. 

stance,  if  you  know  the  three  sides  a,  b,  c,  you  can  make  one  triangle, 
and  only  one,  with  these  sides.  If  you  only  know  the  three  angles 
you  can  make  any  number  of  triangles  with  three  such  angles.  All 
of  them  will  have  the  same  shape,  but  they  will  have  different  sizes. 
(See  Fig.  7.) 

THE  SPHERE  :    ITS   PLANES   AND   CIRCLES. — In  Fig. 
8,  0  is  the   centre   of   the   sphere.      Suppose  any  plane 


SPACE—  THE  CELESTIAL  SPHERE— DEFINITIONS.   25 

as  AB  to  pass  through  the  centre  of  the  sphere.  It  will 
cut  the  sphere  into  two  hemispheres.  It  will  intersect  the 
surface  of  the  sphere  in  a  circle  AEBF  which  is  called  a 
great  circle  of  the  sphere.  A  great  circle  of  the  sphere  is 
one  cut  from  the  surface  by  a  plane  passing  through  the 
centre  of  the  sphere.  Suppose  a  right  line  POP'  perpen- 
dicular to  this  plane.  The  points  P  and  P'  in  which  it 
intersects  the  surface  of  the  sphere  are  every  where  90°  from 
the  circle  AEBF.  They  are  the  poles  of  that  circle.  The 
poles  of  the  great  circle  CEDF  are  Q  and  Q'.  It  is 
proved  in  geometry  that  the  following  relations  exist  be- 
tween the  angles  made  in  the  figure  : 


FIG.  8. — THE  SPHERE  ;  ITS  GHEAT  CIRCLES  ;  THEIR  POLES. 

I.  The  angle  POQ  between  the  poles  is  equal  to  the  in- 
clination of  the  planes  to  each  other. 

II.  The  arc  BD  which  measures  the  greatest  distance 
between  the  two  circles  is   equal   to  the  arc  PQ  which 
measures  the  angle  POQ. 

III.  The  points  E  and  F,  in  which  the  two  great  circles 
intersect  each  other,  are   the   poles   of  the  great   circle 


26  ASTRONOMY. 

PQACP'Q'BD  which  passes  through  the  poles  of  the  first 
two  circles. 

The  Spherical  Triangle. — In  the  last  figure  there  are 
several  spherical  triangles,  as  EDB,  FAC,  ECP'Q'B,  etc. 
In  astronomy  we  need  consider  only  those  whose  sides  are 
formed  by  arcs  of  great  circles.  The  angles  of  the  trian- 
gle are  angles  between  two  arcs  of  great  circles;  or  what  is 
the  same  thing,  they  are  angles  between  the  two  planes 
which  cut  the  two  arcs  from  the  surface  of  the  sphere. 

In  spherical  triangles,  as  in  plane,  there  are  six  parts, 
three  angles  and  three  sides.  Having  any  three  parts  the 
other  three  can  be  constructed. 

The  sides  as  well  as  the  angles  of  spherical  triangles  are 
expressed  in  degrees,  minutes,  and  seconds. 

If  the  student  has  a  school  globe,  let  him  mark  on  it  the  triangle 
whose  sides  are — 

a  =  10°,  6  =  7°,  e  =  4°. 

Its  angles  will  be  (A  is  opposite  to  a,  B  to  b,  C  to  e) : 

A  =  128°  44'  45". I 
B=  83°  11'  12'  0 
C-  18°15'31".l 

LATITUDE  AND  LONGITUDE  OF  A  PLACE  ON  THE 
EAKTH'S  SURFACE. — According  to  geography,  the  latitude 
of  a  place  on  the  Earth's  surface  is  its  angular  distance 
north  or  south  of  the  Earth's  equator. 

Tfie  longitude  of  a  place  on  the  Earth's  surface  is  its  an- 
gular distance  east  or  west  of  a  given  first  meridian  (the 
meridian  of  Greenwich,  for  example). 

If  P  in  Fig.  9  is  the  north  pole  of  the  earth,  the  lat- 
itude of  the  point  B  is  60°  north;  of  Z  it  is  30°  north;  of 
/  it  is  27£°  south.  All  places  having  the  same  latitude  are 
situated  on  the  same  parallel  of  latitude.  In  the  figure 
the  parallels  of  latitude  are  represented  by  straight  lines. 


SPACE— THE  CELESTIAL  SPHERE- DEFINITIONS.   27 

All  places  having  the  same  longitude  are  situated  on  the 
same  meridian.  We  shall  give  the  astronomical  definitions 
of  these  terms  further  on. 

It  is  found  convenient  in  astronomy  to  modify  the  geo- 
graphical definition  of  longitude.  In  geography  we  say 
that  Washington  is  77°  west  of  Greenwich,  and  that  Syd- 
ney (Australia)  is  151°  east  of  Greenwich.  For  astronom- 


Fio.  9.— LATITUDE  AND  LONGITUDE  OP  PLACES  ON  THE  EARTH'S 

SURFACE. 

ical  purposes  it  is  found  more  convenient  to  count  the 
longitude  of  a  place  from  the  first  meridian  always  towards 
the  west.  Thus  Sydney  is  209°  west  of  Greenwich  (360° 
-  151°  =  209°). 

The  Earth  turns  on  its  axis  once  in  24  hours.  In  a  day 
of  24  hours  every  point  on  the  Earth's  surface  moves 
once  round  a  circle  (its  parallel  of  latitude).  Every  point 


28  ASTRONOMT. 

moves  360°  in  24  hoars,  or  at  the  rate  of  15°  every  hour 
(360°  divided  by  24  is  15°). 

Hence  we  can  measure  the  longitude  of  a  place  in  de- 
grees or  in  hours,  just  as  we  choose.  Washington  is  5h  8m 
west  of  Greenwich  (77°)  and  Sydney  is  13h  56m  west  of 
Greenwich  (209°).  In  the  figure  suppose  F  to  be  west  of 
the  first  meridian.  All  the  places  on  the  meridian  PQ 
have  a  longitude  of  15°  or  1  hour  ;  all  those  on  the  merid- 
ian P5h  Q  have  a  longitude  of  75°  or  5  hours  ;  and  so  on. 

—  What  is  an  angle?  What  is  a  degree?  What  is  a  minute  of 
arc?  a  second?  The  radius  of  a  circle,  if  wrapped  around  the  cir- 
cumference of  a  circle,  would  cover  an  arc  of  how  many  degrees? 
What  is  the  angular  diameter  of  the  Moon  ?  of  the  Sun  ?  How  far 
apart  in  arc  are  the  two  "  pointers  "  of  the  Great  Bear?  What  is  the 
difference  between  a  plane  triangle  and  a  spherical  triangle?  Give 
an  example  of  a  plane  triangle  ;  of  a  spherical  triangle.  Define  the 
latitude  of  a  place  on  the  Earth's  surface.  Define  the  longitude  of 
a  place  on  the  Earth's  surface. 

10.  The  Points  and  Circles  of  the  Celestial  Sphere. — 

THE  HORIZOK. — We  only  see 
one  half  of  the  celestial  sphere; 
namely,    the    half   above    our 
heads.     If  we  are  at  sea,  or  in 
a  large  open  country  on  land, 
the  concave  vault  of  the  day- 
time sky  seems  to  rest  on  a  flat 
plain,  and  this  plain  seems  to 
be  bounded  by  a  circle.     The 
flat  plain  is  called  the  plane  of 
Fio.  IO.-HAT,*   OF   THE   CK-  the  horizon  (pronounced  hor-I'- 
LESTIAT,    SPHERE,   STUDDED  Zon).    Its  bounding  circle  is  the 
WITH  STARS.  circle  of  the  horizon.     A  point 

The  sphere  seems  to  rest  on  the  ,  , 

plane  of  the  horizon.   The  horizon  on  the   celestial  sphere  directly 
seems  to  be  bounded  by  the  circle  .  ,  .  , 

NHS.  N  is  the  north  point,  s  is  overhead  is  called  the  zenitn- 

the south  point  of  the  horizon.    Z  .     .   a         .•> 

is  the  zenith-point  or  the  point  point,    or     more     briefly    the 

directly  overhead. 


SPACE— THE  CELESTIAL  SPHERE— DEFINITIONS.   29 

zenith.  A  line  joining  the  observer  and  the  zenith-point 
is  perpendicular  to  the  plane  of  the  horizon.  If  you  wish 
to  describe  the  situation  of  a  star  you  can  say  that  its 
zenith-distance  is  so  many  degrees — 50°  for  example.  The 
star  8  in  the  figure  is  distant  from  the  zenith  Z  by  an  arc 
ZS.  Its  zenith-distance  is  50°.  The  arc  from  the  zenith 
to  the  horizon  is  90°.  That  is,  the  zenith-distance  of  the 
horizon  is  everywhere  90°.  The  altitude  of  a  star  is  its 
angular  distance  above  the  horizon.  The  altitude  of  the 
star  8  in  the  figure  is  HS  =  40°. 

The  zenith-distance  and  the  altitude  of  a  star  are  meas- 
ured on  a  vertical  circle,  i.e.,  on  a  circle  passing  through 
the  star  and  perpendicular  to  the  horizon. 

The  zenith-distance  of  any  star  +  the  altitude  of  the  star  =  90°. 


FIG.  11. — THE  EAKTH'S  Axis  AND  THE  PLANE  OF  ITS 
EQUATOR  EQ. 

NP  is  the  earth's  north  pole ;  SP  is  the  south  pole ;  eq  is  the  earth's 
equator ;  EQ  is  the  plane  of  the  celestial  equator. 


30  ASTRONOMY. 

THE  CELESTIAL  EQUATOR. — In  the  figure  there  is  a  pic- 
ture of  the  Earth.  NP  is  its  north  pole,  SP  is  its  south 
pole,  and  the  line  joining  them  is  the  Earth's  axis,  eq  is 
the  Earth's  equator.  It  is  a  circle  round  the  Earth.  If 
we  imagine  the  plane  of  that  circle  to  continue  out  beyond 
the  Earth  on  all  sides  till  it  reaches  the  celestial  sphere  the 
shaded  surface  EQ  (a  circle)  will  represent  it.  This  sur- 
face is  the  plane  of  the  equator  of  the  celestial  sphere — or 
more  briefly,  it  is  the  plane  of  the  celestial  equator.  If  we 
imagine  the  axis  of  the  earth  prolonged  both  ways  till  it 
meets  the  celestial  sphere  the  prolonged  line  is  the  axis  of 
the  celestial  sphere. 

If  we  imagine  the  planes  of  the  meridians  and  parallels 
on  the  Earth  to  be  prolonged  outwards  to  meet  the  celes- 
tial sphere,  they  will  meet  it  in  circles  that  are  the  merid- 
ians and  parallels  of  that  sphere.  They  are  not  drawn  in 
the  last  figure,  so  as  to  avoid  confusing  it  ;  but  some  of 
them  are  drawn  in  the  next  figure.  In  this  n  is  the  north 
pole  of  the  Earth,  NP  the  north  pole  of  the  celestial 
sphere;  eq  is  the  equator  of  the  Earth,  EQ  the  equator  of 
the  celestial  sphere — the  celestial  equator;  the  plaues  of  the 
meridians  of  the  Earth  are  prolonged  and  make  the  merid- 
ians of  the  celestial  sphere  ;  the  plaues  of  the  parallels  on 
the  Earth  make  the  parallels  ML,  EQ  (for  the  equator  is 
a  parallel  of  latitude),  and  SO. 

Z  is  the  zenith-point  of  the  observer — it  is  the  point  of 
the  celestial  sphere  directly  over  his  head.  JVis  the  nadir- 
point  of  the  observer — it  is  the  point  of  the  celestial  sphere 
directly  beneath  his  feet.  HR  is  a  plane  through  the  cen- 
tre of  the  Earth  and  perpendicular  to  the  line  ZN.  We 
shall  now  define  the  plane  of  the  horizon  to  be  that  plane 
passing  through  the  centre  of  the  Earth  which  is  perpen- 
dicular to  the  line  joining  the  observer's  zenith-  and  nadir- 
points.  On  page  28  the  horizon  was  described  as  the  flat 
plain  on  which  the  observer  stands  and  on  which  the  up- 


SPACE— THE  CELESTIAL  SPHERE— DEFINITIONS.   31 

per  half  of  the  celestial  sphere  rests.  Such  a  plane  is 
called  the  plane  of  the  sensible  horizon  (i.e.,  of  the  horizon 
evident  to  the  senses).  HR  through  the  centre  of  the 
Earth  divides  the  celestial  sphere  into  two  equal  parts.  It 
is  called  the  rational  horizon.  The  sensible  and  the  ra- 
tional horizons  are  parallel  to  each  other. 


FIG.  12. — THE  EARTH  (n,  q,  s,  e)  SURROUNDED  BY  THE  CELESTIAL 
SPHERE  (N,  Q,  S,  E). 

The  meridians  and  parallels  on  the  celestial  sphere  serve 
the  same  purpose  as  the  meridians  and  parallels  on  the 
Earth.  The  latitude  of  a  place  on  the  Earth  is  its  angular 
distance  north  or  south  of  the  terrestrial  equator.  The 
longitude  of  a  place  on  the  Earth  is  the  angular  distance 
of  that  place  west  of  the  first  meridian.  If  we  know  the 


32  ASTRONOMY. 

latitude  and  longitude  of  a  place  on  the  surface  of  the 
Earth  we  know  all  that  can  be  known  of  its  situation. 

Just  in  the  same  way  we  describe  the  situations  of  stars 
on  the  surface  of  the  celestial  sphere.  The  declination  (like 
latitude)  of  a  star  is  its  angular  distance  north  or  south  of 
the  celestial  equator.  The  right-ascension  (like  longi- 
tude) of  a  star  is  its  angular  distance  east  of  the  first  me- 
ridian. Declinations  in  the  sky  are  like  latitudes  on  the 
Earth.  Eight-ascensions  in  the  sky  are  like  longitudes  on 
the  Earth.  The  names  are  different,  but  the  principle  of 
measurement  is  the  same. 

DECLINATION  OF  A  STAR.— The  declination  of  a  star  is 
its  angular  distance  north  or  south  of  the  celestial  equator. 


FIG.  13. — DECLINATION  AND  RIGHT- ASCENSION  OF  A  STAR. 

In  the  figure  EVQ  is  the  equator  of  the  celestial  sphere— the  celes- 
tial equator.  The  Earth  is  not  shown  in  the  picture.  If  it  were 
shown  it  would  be  a  dot  at  the  centre  of  the  sphere.  PAa  is  a  merid. 
ian  of  the  celestial  sphere  passing  through  the  star  A.  The  angular 
distance  of  the  star  A  north  of  the  celestial  equator  is  Aa.  Aa  is 
the  north  declination  of  that  star.  PbB  is  a  meridian  of  the  celestial 
sphere  passing  through  the  star  B.  This  star  is  south  of  the  celes- 
tial equator  by  an  angular  distance  measured  by  bB.  bB  is  the  south 
declination  of  the  star  B. 


SPACE— THE  CELESTIAL  SPHERE— DEFINITIONS.   33 

If  for  a  moment  we  should  take  the  sphere  PEQ  to  represent  the 
Earth  and  EQ  the  equator  of  the  Earth,  then  the  terrestrial  north 
latitude  of  A  would  be  measured  by  aA  and  the  south  latitude  of  B 
by  bB.  The  declination  of  a  point  on  the  surface  of  the  celestial 
sphere  corresponds  to  the  latitude  of  a  point  on  the  surface  of  the 
Earth.  PA  is  the  north  polar-distance  of  A  ;  P'B  is  the  south  polar- 
distance  of  B 

The  polar-distance  of  a  star  +  the  star's  decimation =90*. 

EIGHT-ASCENSION  OF  A  STAR. — The  right-ascension  of  ,1 
star  is  its  angular  distance  east  of  a  first  meridian. 


FIG.  13  Ms. 


In  the  figure  P  V  is  the  first  meridian.  PAa  is  the  meridian 
through  the  star  A.  This  meridian  is  east  of  the  first  meridian  by 
the  angle  VPa,  which  is  measured  by  the  arc  Va.  Va  is  the  right- 
ascension  of  the  star  A.  PbB  is  the  meridian  through  the  star  B. 
This  meridian  is  east  of  the  first  meridian  by  the  angle  VPb,  which 
is  measured  by  the  arc  Vb.  Vb  is  the  right-ascension  of  the  star  B. 

If  for  a  moment  we  should  take  the  sphere  PEQ  to  represent  the 
Earth,  and  EQ  the  equator  of  the  Earth,  and  PV  the  meridian  of 
Greenwich,  (east)  terrestrial  longitude  of  a  place  A  would  be  Va; 
the  longitude  of  a  place  B  would  be  bB.  The  right- ascension  of  a 
point  on  the  surface  of  the  celestial  sphere  corresponds  to  the  longi- 
tude of  a  point  on  the  surface  of  the  Earth. 

It  is  very  important  to  understand  these  matters  at  the  beginning, 


34  ASTRONOMY. 

and  it  is  necessary  for  the  student  to  memorize  the  following  defini- 
tions:— 

The  plane  of  the  horizon  is  a  plane  through  the  centre  of  the  Earth 
perpendicular  to  the  line  joining  the  zenith  and  the  nadir  of  the  ob- 
server. The  zenith  of  an  observer  is  the  point  of  the  celestial  sphere 
directly  over  his  Lead.  Therefore  each  person  has  a  different  zenith- 
point.  The  nadir  of  an  observer  is  the  point  of  the  celestial  sphere 
directly  beneath  his  feet.  The  zenith  and  nadir  are  points  on  the 
surface  of  the  celestial  sphere — not  points  on  the  Earth.  Tliezenii/t- 
distance  of  a  star  is  its  angular  distance  from  the  zenith.  The  alti- 
tude of  a  star  is  its  angular  distance  above  the  horizon.  A  vertical 
circle  is  a  great  circle  of  the  sphere  whose  plane  is  perpendicular  to 
the  plane  of  the  horizon.  The  axis  of  the  celestial  sphere  is  the  line 
of  the  Earth's  axis  prolonged.  The  equator  of  the  celestial  sphere— 
the  celestial  equator— is  that  great  circle  cut  from  the  celestial  sphere 
by  the  plane  or  the  Earth's  equator  extended.  The  declination  of  a 
star  is  its  angular  distance  north  or  south  of  the  celestial  equator. 
The  right- ascension  of  a  star  is  its  angular  distance  east  (not  west)  of 
the  first  meridian  of  the  celestial  sphere.  (This  first  meridian  has 
nothing  to  do  with  the  meridian  of  Greenwich  on  the  Earth,  as  we 
shall  soon  see. ) 

The  terrestrial  meridian  of  an  observer  is  that  great  cir- 
cle of  the  Earth  that  passes  through  the  observer  and 
through  the  Earth's  axis.  All  terrestrial  meridians  pass 
through  the  north  and  south  poles  of  the  Earth. 

The  celestial  meridian  of  an  observer  is  that  great  circle 
of  the  celestial  sphere  that  passes  through  the  zenith  of 
the  observer  and  through  the  axis  of  the  celestial  sphere. 
All  celestial  meridians  pass  through  the  north  and  south 
poles  of  the  celestial  sphere. 

In  figure  14  n,  e,  q,  8  is  the  earth,  and  some  terrestrial  meridians  are 
drawn  upon  it.  Some  celestial  meridians  are  drawn  on  the  celestial 
sphere  NP,  E,  Q,  SP.  Z  is  the  zenith  of  the  observer.  Where  must 
he  be  in  the  figure  ?  He  must  be  on  the  surface  of  n,  e,  q,  s,  where 
aline  ZN (zenith  to  nadir)  intersects  it.  Make  a  pin-prick  at  this 
point.  His  terrestrial  meridian  is  the  little  circle  n,  e,  q,  s  (because 
it  passes  through  the  observer's  place  and  through  n  and  s).  His 
celestial  meridian  is  NP,  Z,  SP  (because  it  contains  his  zenith  and 
the  two  celestial  poles). 


SPACE— THE  CELESTIAL  SPHERE— DEFINITIONS.   35 


FIG.  14.— CORRESPONDENCE  OF  THE  TERRESTRIAL  AND  CELESTIAL 
MERIDIANS  OP  AN  OBSERVER. 


FIG.  15. — THE  CELESTIAL  SPHERE. 


36  ASTRONOMY. 

—  It  is  so  important  for  the  student  to  understand  the  foregoing 
definitions  clearly  that  the  following  exercises  are  added.  The  fig- 
ures have  been  purposely  drawn  unlike  each  other. 

In  figure  15  P  is  the  north  pole  of  the  celestial  sphere  ;  Z  is  the 
observer's  zenith  ;  HE  his  horizon  ;  0  is  the  position  of  the  Earth. 

What  is  the  zenith-distance  of  £?  What  is  the  altitude  of  S? 
What  is  the  altitude  of  Z?  What  is  the  altitude  of  P?  What  is  the 
altitude  of  M ?  (Answers  :  Z8,  TS,  90°,  RP,  HM.)  Notice  that  an 
observer  at  0  looks  along  a  horizontal  line  OT ;  he  sees  the  star  S 
along  the  line  OS  ;  the  angle  TOS  is  the  altitude  of  S,  and  it  is  meas- 
ured by  the  arc  TS.  RH  is  the  observer's  north  and  south  line,  EW 
is  his  east  and  west  line.  His  points  of  the  compass  are  R  =  north, 
E  =  east,  //  —  south,  W  =  west. 


FIG.  16.— THE  CELESTIAL  SPHERE. 

In  figure  16  P  is  the  north  pole  of  the  celestial  sphere,  ECWD 
is  the  celestial  equator  ;  P  V  is  the  first  meridian  of  the  celestial 
sphere.  What  is  the  right-ascension  of  the  point  F?  of  B  ?  of  (7?  of 
Et  of  D1  of  Wt  (Answers  :  0°,  VB,  VG,  VCE,  VCED,  VCEDW.) 
What  are  the  right  ascension  and  declination  of  the  point  A  't  (An- 
swer :  VB  and  north  BA).  What  is  the  altitude  of  A  ?  (Answer  : 
GA.) 


SPACE— THE  CELESTIAL  &PSERE—  DEFINITIONS.   37 

—  What  is  the  horizon  of  an  observer  ?  Can  you  conceive  a  hori- 
zon without  specifying  an  observer's  place?  What  is  a  vertical  line? 
If  you  had  a  string  and  a  bunch  of  keys,  how  could  you  use  them  to 
show  the  vertical  direction  at  your  station  ?  Is  this  direction  the 
same  with  respect  to  each  observer,  no  matter  where  he  is  situ- 
ated ?  Do  you  suppose  this  direction  is  absolutely  the  same  in  space 
for  two  observers  1000  miles  apart  ? 

What  is  the  zenith  of  an  observer  ?  His  nadir  ?  Have  the  words 
zenith  and  nadir  any  meaning  if  no  observer  or  station  is  supposed  ? 
When  you  assume  a  point  on  the  celestial  sphere  as  the  zenith  of  an 
observer,  is  his  place  on  the  earth  fixed?  When  you  assume  the 


FIG.  17. — PART  OF  A  CELESTIAL  GLOBE: 
Showing  the  principal  circles  of  the  celestial  sphere. 

place  of  an  observer  on  the  earth,  is  his  zenith  a  determinate  point 
on  the  celestial  sphere  ?     Or  may  it  be  two  points  ?     What  is  a  star's 
altitude?  its  zenith  distance?     In  an  swering  these  two  questions, 
did  you  say  its  angular  distance  from,  etc.  ? 
In  figure  17  Z  is  the  zenith  of  the  observer  and  NWS  his  hori- 


38  ASTRONOMY. 

zon.  P  is  the  north  celestial  pole.  PZ8  is  the  observer's  celestial 
meridan.  XXI,  XXII  .  .  .  0,  I,  II  ...  is  the  celestial  equator, 
and  0  is  the  vernal  equinox — the  origin  of  right-ascensions.  Paral- 
lels of  declination  are  shown  (circles  parallel  to  the  celestial  equator) 
every  10°  both  north  and  south  of  the  equator.  Meridians  of  the 
celestial  sphere  (hour-circles)  are  drawn  every  15°;  every  hour.  They 
pass  from  pole  to  pole  across  the  celestial  sphere  and  cross  the  equa- 
tor at  the  points  marked  XXI,  XXII,  .  .  .  I,  II  .  .  .  Every  star  on 
the  hour-circle  I  has  a  right  ascension  of  15°,  or  1  hour ;  on  //  of 
30°,  or  2h  ;  on  XXII  of  330°,  or  22  hours  ;  and  so  on. 

All  stars  on  the  parallel  of  declination  marked  A  have  a  north 
declination  of  40°  (+  40°) ;  on  the  parallel  C,  of  +  30°  ;  on  the  equa- 
tor, of  0°  ;  on  the  parallel  Sof—  30°.  The  student  should  mark  the 
following  places  on  the  figure  : 

R.  A.  =  22h  and  Decl.  =  +  80°  ;  R.  A.  =  Oh  and  Decl.  =  -  40°  ; 

=  23h         "          =  -  30° ;  =    lh        "          =  +  60°  ; 

=  24"        "           =0°;  =   2»                    =  +  40°; 

=   oh        "          =  +  40°  ;  =  2*        "          =  -  30'. 


CHAPTER  III 
DIURNAL  MOTION  OF  THE  SUN,   MOON,   AND  STARS. 

11.  The  Diurnal  Motion  of  the  Sun,  Moon,  and  Stars. — 

It  is  a  familiar  fact  to  all  of  us  that  the  Sun  rises  and  sets 
every  day.  The  Moon  rises  and  sets.  Stars  also  rise  above 
the  eastern  horizon;  they  appear  to  move  across  the  sky 
and  to  come  to  their  greatest  altitude  on  the  meridian  ; 


FIG.  18. — THE  APPARENT  MOTION  OF  THE  SUN  FROM  RISING  TO 

SETTING. 


and  then  they  appear  to  decline  to  the  west  and  set  below 
the  western  horizon.  Every  one  is  familiar  with  the  Sun's 
rising  and  setting.  It  is  too  splendid  a  spectacle  to  be 
overlooked.  We  are  all  more  or  less  familiar  with  the  mo- 
tion of  the  Moon  from  rising  to  setting.  We  may  know 

39 


40  ASTRONOMY. 

the  fact  that  groups  of  stars  also  rise  and  set.  But  to  thor- 
oughly understand  their  motions  we  must  actually  observe 
some  particular  stars  carefully.  The  student  should  him- 
self make  the  observations  that  are  described  here  so  far  as 
his  time  and  opportunities  will  allow. 

DIURNAL  MOTIONS  OF  SOUTHERN  STARS. — Let  the 
student  go  out  into  a  field  or  park  at  night  where  he  can 
see  the  sky  from  his  zenith  towards  the  southern  horizon, 

III 


IV 


FIG.  19.— DIURNAL  MOTION  OF  A  GROUP  OF  SOUTHERN  STARS. 
The  right  hand  of  this  picture  is  west :  the  left  hand  is  east. 


and  where  he  can  command  an  unobstructed  view  of  the 
eastern  and  western  horizon.  Let  him  select  a  group  of 
bright  stars  that  are  not  very  far  apart,  and  that  are  not 
very  far  above  the  eastern  horizon.  He  must  learn  the 
group  so  well  that  he  can  always  recognize  it  in  the  sky  no 
matter  where  it  may  be.  Let  him  stand  with  his  back 
toward  the  north.  The  group  is  rising,  let  us  say  (the 
lower  left-hand  circle  in  Fig.  19)  when  he  begins  to 


DIURNAL  MOTION:   SUN,   MOON,  AND  STARS.    41 

observe  it.  If  he  watches  the  group — looking  at  it  every 
half  hour  or  so — he  will  see  that  it  is  continually  rising 
above  the  eastern  horizon  and  getting  higher  in  the  heav- 
ens. 

About  three  hours  after  the  rising  of  this  group  it 
will  be  towards  the  southeast  (the  second  circle  counting 
from  the  left  of  Fig.  19).  About  six  hours  after  rising, 
the  group  will  be  just  south  of  him  and  at  its  highest 
— at  its  greatest  altitude.  The  point  in  the  sky  where  a 
star  (or  a  group  of  stars)  has  its  greatest  altitude  is  called 
its  point  of  culmination.  It  is  due  south  of  the  observer 
at  culmination  (the  uppermost  circle,  S9  in  the  last  figure). 
It  requires  about  six  hours  for  a  group  of  southern  stars  to 
move  from  the  eastern  horizon,  where  it  rises,  to  the  point 
due  south,  where  it  culminates.  Six  hours  of  watching  is 
quite  as  long  as  can  be  given  by  the  student.  But  if  he 
should  watch  longer  than  this,  he  would  see  the  group  of 
stars  decline  to  the  west  and  finally  set  (as  in  the  two  right- 
hand  circles  of  the  last  figure). 

Hunters,  sailors,  shepherds,  as  well  as  astronomers,  have 
observed  facts  like  these  thousands  and  thousands  of  times. 
Any  one  who  wishes  can  observe  them  whenever  he  likes  on 
any  clear  night.  So  that  the  student  can  prove  them  for 
himself  if  he  chooses;  and  we  may  take  them  as  proved 
facts.  The  picture  shows  what  actually  does  happen  for  a 
group  of  southern  stars.  When  it  is  due  south  it  looks 
like  the  upper  circle,  marked  S.  It  is  at  its  culmination. 
It  is  at  its  greatest  altitude.  Three  hours  before  the  time 
of  culmination  the  group  was  as  in  the  circle  next  S,  to 
the  left.  Six  hours  before  this  time  it  was  as  in  the  lower 
left-hand  circle.  Three  hours  after  the  time  of  culmina- 
tion the  group  has  declined  towards  the  west  (see  the 
figure),  and  six  hours  after  this  time  it  is  setting  in  the 
west,  as  in  number  V. 

It  is  not  to  be  expected  that  a  schoolboy  will  have  the 


42  ASTRONOMY. 

leisure  to  watch  throughout  a  whole  night.  If  he  were  to 
do  so  he  would  see  the  group  move  as  in  the  figure  if  he 
used  a  long  winter's  night  for  his  observation  and  began 
his  watch  as  soon  as  the  sky  grew  dark.  There  is  a  sim- 
ple experiment  that  he  can  try,  however,  which  will  make 
the  diurnal  motion  of  the  southern  stars  quite  easy  to  un- 
derstand. Let  him  provide  himself  with  a  hammer  and 
with  a  bundle  of  common  laths,  and  let  him  sharpen  one 
end  of  each  lath  so  that  it  can  be  easily  driven  into  the 
ground.  Let  him  choose  a  spot  of  ground  to  stand  on  that 
is  soft,  so  that  the  laths  can  be  set  in  place  without  too 
much  trouble.  Let  him  select  some  one  bright  star  that 
is  near  the  eastern  horizon,  and  remember  it  well  so  as 
not  to  mistake  it  for  any  other  star. 

Now  he  should  kneel  down,  set  the  sharp  end  of  a  lath 
on  the  ground,  and  sight  along  the  lath  until  it  points  ex- 
actly to  the  star.  The  lath  is  to  be  sighted  at  the  star  just 
as  a  rifle  is  pointed  at  a  deer.  The  lath  is  now  to  be  driv- 
en into  the  ground  firmly;  and  after  this  is  done  it  is  well 
to  take  another  sight  along  the  lath  at  the  star  to  be  sure 
that  it  still  points  correctly.  When  all  is  right  the  ob- 
server should  look  at  his  watch  and  note  the  time  and 
write  it  down,  like  this: 

First  lath  set  at  8h  Om  P.M. 

Things  will  look  as  in  Fig.  20.  The  lath  01  will 
point  to  the  star  at  8h  Om. 

The  observer  need  pay  no  more  attention  to  the  star  for 
a  couple  of  hours.  A  little  before  ten  o'clock  he  should 
take  another  lath  and  make  the  same  observation  on  the 
same  star.  He  will  find  that  the  star  has  moved  towards 
the  west  and  upwards.  Leaving  the  first  lath  in  place,  he 
must  now  fix  a  second  one  so  as  to  point  at  the  star  at  10 
o'clock.  Its  point  will  have  to  be  set  a  few  inches  away 


DIURNAL  MOTION:   SUN,  MOON,  AND  STARS.    43 


East 


West 


The 


Ground 


0 
FIG.  20. — A  POINTER  DIRECTED  AT  A  STAR. 


East 


West 


The 


Ground 


0 
FIG.  21.—  A  POINTER  DIRECTED  AT  A  STAB. 


III 


East 


The 


West 


Ground 


0 
FIG.  22. — A  POINTER  DIRECTED  AT  A  STAR. 


44  ASTRONOMY. 

from  the  point  of  the  first  one,  so  as  not  to  interfere  with 
it.     It  will  appear  as  in  Fig.  21. 

He  should  make  a  second  record,  thus : 

Second  lath  set  at  10h  Ora  P.M. 

Now  the  observer  can  go  to  sleep  if  he  likes,  setting 
his  alarm-clock  to  wake  him  about  quarter  before  twelve. 
At  12h  he  should  set  a  third  lath  to  point  at  the  same  star. 
It  will  be  like  Fig.  22. 

His  note-book  will  read : 

Third  lath  set  at  12h  Om  P.M. 

He  should  do  the  same  thing  at  2  o'clock  in  the  morning, 
and  the  fourth  lath  will  point  as  in  the  next  figure. 

Fourth  lath  set  at  2  A.M. 


East  /  West 


The [_ Ground 

O 
FIG.  23. — A  POINTER  DIRECTED  AT  A  STAR. 

These  four  observations  will  be  enough,  though  the  more 
that  are  made  the  clearer  the  motion  of  the  star  will  be. 
The  chief  practical  trouble  will  be  that  the  points  of  the 
laths  cannot  be  set  very  close  together  without  interfering 
with  each  other.  If  they  could  be  set  just  right  and  if  a 
great  number  of  them  were  so  set,  things  would  look  like 
the  group  of  laths,  B,  in  the  next  figure,  where  the  flat 


DIURNAL  MOTION:    SUN,   MOON,  AND  STARS.    45 

table  represents  the  ground,  and  the  lines  in  the  circle  B 
represent  a  number  of  laths  accurately  set  at  the  point  0. 

This  figure  makes  everything  clear.  The  laths  have 
been  set  at  equal  intervals  of  time  and  they  are  at  equal 
angles  apart.  This  proves  that  the  apparent  motion  of  the 
star  B  is  such  that  it  moves  through  equal  angles  in  equal 
times.  Its  motion  is  uniform. 

If  the  observer  had  chosen  to  select  a  star  very  far  south 
(A,  for  example)  and  had  set  laths  for  it,  also,  the  group 


FIG.  24  —A  MODEL  TO  SHOW  HOW  STARS  SEEM  TO  MOVE  FROM 
RISING  TO  SETTING  IN  THEIR  DIURNAL  PATHS. 

of  pointers  for  this  star  would  look  like  the  cone  of  rays 
marked  A  in  the  figure.  All  the  laths  would  lie  in  the 
surface  of  a  cone,  and  the  vertex  of  this  cone  would 
be  at  0.  If  he  had  chosen  a  star  nearer  to  his  zenith 
((7,  for  example)  and  had  set  the  laths  for  it,  just  as 
before,  they  would  also  lie  in  the  surface  of  a  cone  (7,  as 
in  the  figure.  Finally,  if  he  had  chosen  a  star  much  fur- 
ther north  (Z>,  for  example)  the  pointers  to  that  star  would 
all  lie  in  the  cone  D.  The  line  OP  is  the  axis  of  all  these 
cones,  and  it  points  to  the  north  pole  of  the  heavens. 


46 


ASTRONOMY. 


The  north  pole  of  the  heavens  is  that  point  ivhere  the  axis 
of  the  Earth,  prolonged,  meets  the  celestial  sphere. 

DIURNAL  MOTIONS  OF  NORTHERN  STARS. — After  the 
motions  of  southern  stars,  from  their  rising  to  their  setting, 
have  been  carefully  observed  and  are  thoroughly  under- 


FIG.  25. — THE  NORTHERN  HEAVENS; 

as  they  appear  to  an  observer  in  the  United  States  in  the  early  evening 
during  August.    The  right-hand  side  of  the  picture  is  east. 

stood,  the  motions  of  northern  stars  must  be  observed. 
They  can  be  studied  in  the  same  way  as  before.  The 
drawings  of  the  cones  C  and  D  in  the  last  figure  show  ex- 
actly what  would  be  observed.  In  every  one  of  these 
cones,  for  any  and  every  star  in  the  sky,  experiments  will 


DIURNAL  MOTION:    SUN,   MOON,  AND  STARS.    47 

prove  that  the  star  moves  through  equal  angles  in  equal 
times.  The  diurnal  motions  of  all  the  stars  are  uniform. 

The  time  required  for  the  star  D  to  go  completely  round 
its  cone  once  and  to  come  back  to  the  starting-point  again 
is  24  hours,  one  day;  and  the  same  is  true  for  any  and 
every  star. 

In  Fig.  25  the  stars  of  the  northern  sky  are  shown 
as  they  appear  to  an  observer  in  the  middle  regions  of  the 
United  States  in  the  early  evening  in  August.  The  same 
stars  are  visible  all  the  year  round,  but  they  will  not  always 
be  at  the  same  altitudes  above  the  horizon  at  the  same  hour 
of  the  night.  No  matter  what  hour  of  the  night,  or  what 
time  of  the  year  you  read  this  paragraph,  you  can  see  the 
stars  of  this  picture  (if  the  night  is  clear)  by  going — now 
— out-of-doors  and  looking  towards  the  north.  In  order  to 
make  the  picture  look  right  you  may  have  to  turn  the  page 
of  the  book  round  somewhat  (in  the  direction  of  the  arrows) 
so  as  to  put  a  different  part  of  the  page  uppermost.  But 
by  taking  a  little  pains  you  can  hold  the  picture  in  such  a 
position  that  it  will  agree  with  the  configuration  of  the 
stars  in  the  sky. 

The  first  set  of  stars  to  find  in  the  sky  is  the  Great  Bear 
• —  Ursa  Major — the  Great  Dipper,  as  it  is  often  called.  It 
is  made  up  of  seven  stars  arranged  somewhat  as  in  the 
next  figure: 

j  #  Polaris. 


*          «  *« 


FIG.  26.  —  URSA  MAJOR  AND  POLARIS. 


48  ASTRONOMY. 

They  are  called  by  these  names  :  a  (Alpha)  Ursae  ma- 
joris;  ft  (Beta)  Ursae  majoris;  y  (Gamma)  Ursae  majoris; 
6  (Delta)  Ursae  majoris;  e  (Epsiloti)  Ursae  majoris  ;  TI 
(Eta)  Ursae  majoris;  C  (Zetd)  Ursae  majoris.  The  letters 
a,  /3,  y,  d,  e,  rj,  C  are  the  first  seven  letters  of  the  Greek 
alphabet.  The  stars  themselves  are  a  part  of  the  constel- 
lation or  group  of  stars  named  Ursa  Major — the  Great  Bear 
— by  the  ancients  (see  Fig.  25).  After  you  have  found 
them  you  must  notice  that  two  of  them  a  and  ft  (they  are 
called  "the  pointers")  point  to  another  star,  not  so 
bright,  which  is  itself  called  Polaris — the  pole-star — the 
star  near  the  north  pole  of  the  celestial  sphere. 

It  is  well  to  form  the  habit  of  glancing  up  at  the  north- 


FIG.  27.— THE  STABS  OF  THE  DIPPER; 
as  they  appear  in  the  early  hours  of  the  evening  in  the  month  of  May. 

ern  heavens  every  time  you  go  out  of  doors  on  a  clear 
night,  so  as  to  be  able  to  find  Ursa  Major,  Polaris,  and 
Cassiopea  quickly  and  easily. 

If  yon  study  the  motions  of  the  northern  stars  you  will 
find  that  Polaris — the  polar  star — seems  to  be  almost  sta- 
tionary. If  it  were  exactly  at  the  north  pole  of  the  heav- 
ens (which  it  is  not)  it  would  be  absolutely  stationary;  but 
it  is  very  nearly  so.  All  the  other  northern  stars  seem  to 


DIURNAL  MOTION:    SUN,  MOON,   AND  STARS.    49 

move  ronud  Polaris  in  circles.  They  move  from  the  east, 
then  upwards,  then  to  the  west,  then  downwards,  then  to 
the  east  again  (in  the  direction  of  the  arrows  in  Fig.  25), 
and  so  on  forever.  It  takes  24  hoars  for  each  and  every 
star  to  move  once  completely  round  the  pole.  Its  motion 
has  a  period  of  one  day — hence  the  name  diurnal  motion. 
The  diurnal  motions  of  all  the  stars  can  be  described  in 
three  theorems  (following) ,  and  you  should  learn  these  the- 
orems by  heart,  because  that  is  the  quickest  way  to  get  a 
perfectly  definite  and  correct  statement  of  the  appearances 
in  the  sky.  Recollect  that  the  north-polar- distance 
(N.P.D.)  of  a  star  is  its  angular  distance  from  the  north 


The  following  are  the  laws  of  the  diurnal  motion: 

I.  Every  star  in  the  heavens  appears  to  describe  a  circle 
around  the  pole  as  a  centre  in  consequence  of  the  diurnal 
motion. 

II.  The  greater  the  star's  north-polar- distance  the  larger 
is  the  circle. 

III.  All  the  stars  describe  their   diurnal  orbits  in  the 
same  period  of  time,  which  is  the  time  required  for  the  earth 
to  turn  once  on  its  axis  (twenty-four  hours). 

These  laws  are  true  of  the  thousands  of  stars  visible  to 
the  naked  eye,  and  of  the  millions  upon  millions  seen  by 
the  telescope. 

The  circle  which  a  star  appears  to  describe  in  the  sky  in 
consequence  of  the  diurnal  motion  of  the  earth  is  called 
the  diurnal  orbit  of  that  star  (an  orbit  is  a  path  in  the 
sky). 

These  laws  are  proved  by  observation.  The  student  can 
satisfy  himself  of  their  correctness  on  any  clear  night. 

If  the  star's  north-polar-distance  is  less  than  the  altitude 
of  the  pole,  the  circle  which  the  star  describes  will  not 
meet  the  horizon  at  all,  and  the  star  will  therefore  neither 
rise  nor  set,  but  will  simply  perform  an  apparent  diurnal 


50  ASTRONOMY. 

revelation  round  the  pole.  Such  stars  are  shown  in 
Fig.  25.  The  apparent  diurnal  motion  of  the  stars  is  in 
the  direction  shown  by  the  arrows  in  the  cut.  Below  the 
north  pole  the  stars  appear  to  move  from  left  to  right,  west 
to  east  ;  above  the  pole  they  appear  to  move  from  east  to 
west. 

The  circle  within  which  the  stars  neither  rise  nor  set  is 
called  the  circle  of  perpetual  apparition.     Within  it  the 


FIG.  28. — THE  STARS  OF  THE  DIPPER; 

as  they  appear  at  different  times  during  their  daily  revolution  round 
the  pole. 

stars  perpetually  appear — are  visible.  The  radius  of  this 
circle  is  equal  to  the  altitude  of  the  pole  above  the  horizon 
or  to  the  north-polar-distance  of  the  north  point  of  the 
horizon. 

When  a  photographic  camera  is  directed  to  the  north 
pole  of  the  heavens  at  night  and  an  exposure  of  about  12 
hours  is  given  the  developed  plate  will  look  like  Fig.  29. 


DIURNAL  MOTION:    SUN,   MOON.  AND  STARS.    51 

The  plate  has  remained  stationary;  the  stars  have  in  12 
hours  moved  one-half  round  their  diurnal  orbits.  In 
moving  they  have  left  " trails"  on  the  plate.  Each  trail 
is  an  arc  of  a  circle,  and  the  centre  of  all  these  circles  is 


FIG.  29. 

From  a  photograph  of  the  motion  of  the  stars  near  the  north  p6le  of  the 
heavens.  The  exposure-time  was  12  hours.  The  bright  trail  nearest  the 
pole  was  made  by  Polaris. 

the  same.  It  is  the  north  celestial  pole.  If  the  camera 
had  been  directed  to  the  equator  the  trails  of  the  stars 
passing  across  the  plate  would  have  been  straight  lines. 


52  ASTRONOMY. 

If  the  student  is  a  photographer,  he  should  try  these  ex- 
periments for  himself,  using  the  longest-focus  lens  that  he 
can  obtain. 

We  have  now  to  inquire  why  do  the  stars  rise  and  set  ac- 
cording to  these  laws.  What  explanations  can  be  given  of 
their  motions  ?  Of  all  the  possible  explanations,  which  is 


FIG.  30. 

From  a  photograph  of  the  trails  of  stars  near  the  celestial  equator. 

the  right  one  ?  It  is  possible  to  explain  the  rising  and  set- 
ting of  the  stars  in  several  ways.  Let  us  give  three  such 
ways. 

(A.)  The  Earth  and  the  observer  are  at  rest  and  each  and 
every  star  has  a  particular  motion  of  its  own,  each  star 


DIURNAL  MOTION:    SUN,   MOON,  AND  STARS.     53 

moving  at  just  such  a  rate  as  actually  to  move  completely 
round  the  Earth  back  to  its  starting-point  in  24  hours. 
There  are  at  least  a  hundred  million  stars,  in  all  possible 
situations.  It  is  incredible  that  each  one  of  them  has  a 
special  rate  of  motion  of  its  own — just  as  a  railway  train 
has  its  own  rate  of  motion — and  that  the  100,000,000  mo- 
tions are  so  nicely  regulated  as  to  obey  the  laws  of  the  di- 
urnal motion  exactly.  This  explanation  is  too  complicated. 
It  must  be  rejected. 

(J9.)  All  the  stars  are  set  in  a  huge  sphere  above  us  ;  all 
of  them  are  at  the  same  distance  from  us;  the  sphere  itself 
turns  round  the  Earth  once  in  24  hours,  while  the  Earth 
and  the  observer  remain  at  rest.  This  was  the  explanation 
given  by  the  ancients  and  it  was  a  perfectly  good  explana- 
tion so  long  as  it  was  not  known  that  the  stars  were  sit- 
uated at  very  different  distances  from  us;  so  long  as  it  was 
not  known  that  some  stars  were  comparatively  near  and 
some  much  further  off.  As  soon  as  we  know  this  one  fact 
it  is  impossible  to  suppose  the  stars  to  be  set  all  in  one 
sphere.  There  would  need  to  be  a  sphere  for  each  star 
(since  no  two  stars  are  at  exactly  the  same  distance  from 
us).  Moreover  the  planets  ( Venus,  Jupiter,  etc.)  and  the 
comets,  are  sometimes  at  one  distance  from  us  and  some- 
times at  another.  So  that  the  explanation  adopted  by  the 
ancients  must  also  be  given  up,  since  the  planets  and  comets 
rise  and  set  like  the  stars. 

(0.)  The  simplest  explanation  possible  is  that  the  stars 
are  fixed  and  do  not  move  at  all  ;  that  the  whole  Earth 
with  the  observer  on  its  surface  revolves  round  an  axis  once 
every  24  hours;  so  that  the  actual  turning  of  the  Earth 
from  west  to  east  makes  the  stars  (and  the  planets  and 
comets)  appear  to  move  from  east  to  west — from  rising  to 
setting.  This  is  the  true  explanation.  It  is  not  true  be- 
cause it  is  the  simplest  ;  nor  is  there  any  one  simple  and 
conclusive  proof  of  its  truth.  It  is  true  because  it  com- 


54:  ASTRONOMY. 

pletely  and  thoroughly  explains  every  single  one  of  millions 
and  millions  of  cases — some  of  them  very  different  from 
others.  There  are  some  rather  complicated  proofs  of  it, 
but  no  simple  ones  suitable  to  be  given  here.  We  must 
accept  it  as.  true  because  it  explains  completely  and  thor- 
oughly every  case  that  has  arisen  in  the  past  and  because 
there  are  millions  and  millions  of  such  cases.  Or,  let  us 
say  that  we  will  accept  it  as  true  until  we  come  to  some 
case  which  is  not  explained  by  it. 


FIG.  31. 

The  real  motion  of  the  horizon  of  an  observer  among  the  stars  makes 
them  appear  to  rise  and  set. 

The  observer  on  the  Earth  is  unconscious  of  its  rotation, 
and  the  celestial  sphere  appears  to  him  to  revolve  from 
east  to  west  around  the  Earth,  while  the  Earth  appears  to 
remain  at  rest.  The  case  is  much  the  same  as  if  he  were 
on  a  steamer  which  was  turning  round,  and  as  if  he  saw  the 
harbor-shores,  the  ships,  and  the  houses  apparently  turn- 
ing in  an  opposite  direction. 


DIURNAL  MOTION:    SUN,   MOON,  AND  STARS.     55 

Fig.  31  is  intended  to  explain  the  apparent  diurnal  motion  of 
the  stars  which  is  caused  by  the  real  rotation  of  the  Earth  on  its  axis. 
The  little  circle  N  is  the  Earth,  seen  as  it  would  be  by  a  spectator 
very  far  away.  The  circle  WZEis  one  of  the  circles  of  the  celestial 
sphere.  W  is  towards  the  west  and  E  towards  the  east.  The  Earth 
revolves  from  west  to  east  in  the  direction  of  the  arrow.  Suppose  a 
to  be  the  situation  of  an  observer  on  the  Earth.  Z  will  be  his  zenith 
in  the  heavens.  HH  will  be  his  horizon  (since  it  is  a  plane  through 
tha  cemtre  of  the  Earth  perpendicular  to  the  line  joining  his  zenith 
and  nadir).  After  a  while  the  observer  will  have  been  carried  on- 
wards by  the  rotation  of  the  Earth  and  his  zenith  will  be  at  Zl '.  His 
horizon  will  have  moved  to  HHf,  It  will  have  moved  below  all  the 
stars  in  the  space  HEH',  and  these  stars  will  have  "  risen  " — 
they  will  have  come  above  his  horizon.  His  horizon  will  have 
moved  above  all  the  stars  in  the  space  HWH'  and  these  stars 
will  have  "  set  "—they  wilt  have  sunk  below  his  horizon. 

It  is  really  the  horizon  that  moves  and  the  stars  that  are  at 
rest  ;  but  in  common  language  we  say  that  one  group  of  stars 
has  risen  above  his  horizon,  and  that  the  second  group  has  set.  A 
little  later  the  observer  on  the  rotating  Earth  will  be  at  the  point  b  ; 
his  zenith  will  be  at  Z'  and  his  horizon  at  H"H".  His  horizon  will 
have  sunk  below  a  new  group  of  stars  in  the  east  (and  these  stars  will 
have  "risen");  and  his  horizon  will  have  moved  above  a  group  of 
stars  in  the  west  (and  this  group  will  have  "  set  "). 

The  zenith  of  an  observer  moves  once  round  the  celestial  sphere 
each  day.  His  horizon  (which  is  perpendicular  to  the  line  joining 
his  zenith  and  nadir)  moves  once  round  the  celestial  sphere  each 
day,  likewise.  Therefore,  stars  in  the  east  rise,  culminate  (come  to 
their  greatest  altitude),  and  set  daily.  This  is  the  apparent  diurnal 
motion  of  the  stars,  and  it  is  explained  by  the  actual  motion  of  the 
Earth  on  its  axis. 

Before  leaving  this  figure  one  important  thing  must  be  noticed. 
Suppose  there  are  two  observers  on  the  Earth,  one  at  a  and  one  at  b. 
Their  zeniths  would  be  at  Z  and  at  Z"  on  the  celestial  sphere  at 
some  ^instant.  Their  horizons  would  be,  at  this  instant,  HH  and 
H''H".  The  observer  to  the  eastward  (b)  would  see  a  whole  group  of 
stars  that  are  yet  invisible  to  the  other  observer  further  west  (a). 
That  is,  an  observer  at  Greenwich  at  ten  o'clock  at  night  (for  ex- 
ample) will  see  groups  of  stars  then  invisible  to  an  observer  at 
Washington.  The  horizon  of  the  Washington  observer  has  not  yet 
moved  below  them  ;  they  have  not  yet  risen  to  him.  If  the  Wash- 
ington observer  waits  for  several  hours  these  groups  will,  by  and  by, 


56  ASTRONOMY. 

rise.     But  the  Greenwich  observer  always  sees  stars  rise  before  they 
have  risen  at  Washington. 

—  What  is  the  diurnal  motion  of  the  stars  ?  Describe  the  course  of 
a  southern  star  from  its  rising  to  its  setting.  At  what  point  does  such 
a  star  attain  its  greatest  altitude  above  the  horizon  ?  What  number 
will  express  the  altitude  (in  degrees,  for  instance)  of  a  star  when  it 
is  rising?  What  is  the  point  of  culmination  of  a  star?  The  word 
culmination  is  often  used  to  express  a  time  as  well  as  a  definite  point 
in  the  sky — what  time  ?  How  can  stakes  set  in  the  ground  be  used 
to  demonstrate  the  diurnal  motion  of  the  stars?  Is  the  motion  of  the 
stars  from  rising  to  setting  uniform?  How  do  you  know?  The 
southern  stars  all  rise  and  set.  What  stars  do  not  rise  and  set? 
What  stars,  then,  are  always  above  the  observer's  horizon  ?  The 
north-polar-distance  of  every  star  that  never  sets  must  be  less  than 
the  altitude  of — what  point  ?  Make  a  sketch  of  the  seven  stars  of 
the  Great  Bear.  Which  two  are  the  pointers  ?  Where  would  Polaris 
be  in  this  sketch  ?  Hold  the  paper  on  which  the  sketch  is  made  be- 
tween the  thumb  and  finger  of  your  left  hand  with  Polaris  covered 
by  your  thumb.  Now  turn  the  paper  round  slowly,  taking  hold  of 
the  outer  edges  of  it.  If  you  face  the  north  while  doing  this  you 
will  see  that  you  are  imitating,  by  a  model,  the  actual  diurnal  mo- 
tions of  the  northern  stars.  Define  the  north  pole  of  the  heavens.  In 
which  direction  (west  to  east,  or  east  to  west)  do  such  stars  move 
when  they  are  above  the  pole?  When  they  are  below  below  the  pole  ? 
How  do  they  move  (up  or  down  ?)  when  they  are  furthest  east  ?  Fur- 
thest west  ? 

Define  in  a  brief  and  accurate  phrase  the  north-polar-distance  in 
stars? 

Give  the  three  laws  of  the  diurnal  motion.     I.  Every  star  in  the 

heavens .     II.  The  greater  the  star's  N.P.D.  III.  All 

the  stars  describe  their  diurnal  orbits  in  the  same ,  which  is  the 

?   What  is  the  diurnal  orbit  of  a  star?    How  can  you  know  that 

these  laws  are  true?     What  is  the  circle  of  perpetual  apparition? 
Why  is  it  so  called? 

The  foregoing  laws,  I,  II,  III,  are  true,  as  we  know  from  observa- 
tion. These  are  the  appearances.  What  is  the  real  cause  of  these 
appearances?  How  do  we  know  that  the  stars  are  not  actually  set  in 
a  huge  sphere  above  our  heads,  and  that  this  sphere  does  not  turn 
around  the  fixed  Earth  once  every  day  ?  (motions  of  planets,  comets, 
etc.)  The  Earth  turns  on  its  axis  once  in  24  hours — do  you  feel  it 
turning  ?  If  the  Earth  turns,  and  the  observer  stays  at  one  place  (say 
in  New  York)  on  its  surface,  does  he  move  in  space  ?  If  the  observer 


DIURNAL  MOTION:    SUN,   MOON,   AND  STARS.     57 

moves  round  a  circle  every  day,  will  liis  zenith  move  on  the  surface 
of  the  celestial  sphere?  his  nadir?  Will  his  horizon  move  among  the 
stars?  When  his  horizon  moves  below  a  group  of  stars  in  the  east, 

those  stars  will ?     When  his  horizon  moves  above  a  group  of 

stars  in  the  west  those  stars  will ? 


FIG.  32. — PART  OF  A  CELESTIAL  GLOBE: 
Showing  the  principal  circles  of  the  celestial  sphere. 


In  this  figure  Z  is  the  zenith  of  the  observer,  and  .ZVWS'his  horizon. 
P  is  the  north  celestial  pole,  and  XX,  XXI  .  .  .  0,  I  .  .  .  the  celes- 
tial equator.  0  is  the  vernal  equinox.  All  stars  on  the  hour  circle 
of  II  hours  are  on  the  celestial  meridian  of  the  observer  (PZS).  The 
star  C  (whose  R.A.=  22h)  is  4  hours  west  of  the  meridian  ;  the  star 
D  (R.  A.  =  20h)  is  6h  west — nearly  to  the  western  horizon. 

In  Fig.  33  Z,  P,  NWS,  etc.,  have  the  same  meaning  as  in  Fig. 
32.  In  fact,  the  picture  represents  the  same  globe  after  it  has 
been  turned  one  hour  towards  the  west.  The  stars  C  and  D  are 
in  the  same  places  on  the  celestial  sphere  as  before,  but  C  is  now  5h 


58  ASTRONOMY. 

west  of  the  meridian,  and  D  is  just  setting  7h  west  of  the  meridian. 
In  Fig.  32  A  and  B  (whose  right  ascensions  are  2h)  were  on  the 
celestial  meridian  of  the  observer ;  here  they  are  lh  west  of  the 
meridian. 


N  FIG.  33.— PART  OP  A  GLOBE: 
Showing  the  principal  circles  of  the  celestial  sphere. 


CHAPTER  IV. 

THE  DIURNAL    MOTION    TO    OBSERVERS    IN    DIFFERENT 
LATITUDES,    ETC. 

12.  The  Latitude  of  an  Observer  on  the  Earth. — The  al- 
titude of  the  celestial  pole  above  the  horizon  of  any  place  on 
the  Earth's  surface  is  equal  to  the  latitude  of  that  place. 

Let  L  be  a  place  on  the  Earth  PEpQ,  Pp  being  the 
Earth's  axis  and  EQ  its  equator.  Z  is  the  zenith  of  the 
place,  and  HR  its  sensible  horizon.  Its  celestial  or  rational 


FIG.  34. 


horizon  would  be  represented  by  a  line  through  0  parallel 
to  HR.  LOQ  is  the  latitude  of  L  according  to  ordi- 
nary geographical  definitions  ;  i.e.,  it  is  the  angular 
distance  of  L  from  the  Earth's  equator.  Prolong  OP  in- 
definitely to  P'  and  draw  LP"  parallel  to  it.  P'  and  P" 


60  ASTRONOMY. 

are  points  on  the  celestial  sphere  infinitely  distant  from  L. 
In  fact  they  appear  as  one  point  ;  since  the  dimensions  of 
the  Earth  are  vanishingly  small  compared  with  the  radins 
of  the  celestial  sphere.*  "We  have  then  to  prove  that 
LOQ  =  P"LH. 

POQ  and  ZLH  are  right  angles,  and  therefore  equal. 
ZLP"  =  ZOP'  by  construction.  Hence  ZLH-  ZLP" 
=  P"LH=  POQ  -  ZOP'  =  LOQ,  or  the  latitude  of  the 
point  L  is  measured  by  either  of  the  equal  angles  LOQ  or 
P"LH. 

In  Geography,  which  deals  only  with  the  Earth,  it  is 
convenient  to  define  the  latitude  of  an  observer  anywhere 
on  the  surface  to  be  the  angular  distance  of  the  point 
where  he  stands  from  the  terrestrial  equator.  The  lati- 
tude of  an  observer  at  L  is  LOQ  . 

In  Astronomy,  which  deals  chiefly  with  the  heavens,  it 
is  convenient  to  define  the  latitude  of  an  observer  anywhere 
on  the  Earth's  surface  to  be  the  altitude  of  his  celestial  pole 
above  his  horizon.  The  latitude  of  an  observer  at  L  is 
P"LH  =  the  altitude  of  the  pole  ;  or  we  might  say,  the  lat- 
itude of  an  observer  is  the  N.P.D.  of  tho  north  point  of 
his  horizon  (if  he  is  in  the  northern  hemisphere).  The 
latitude  of  an  observer  at  L  is  P"LH  in  Fig.  34. 

It  is  often  more  convenient,  in  Astronomy,  to  define  the 
latitude  of  an  observer  by  describing  the  place  of  his  zenith 
on  the  celestial  sphere — and  to  say,  the  latitude  of  an  ob- 
server anywhere  on  the  Earth's  surface  is  the  declination 
of  his  zenith. 

Fig.  35  represents  the  celestial  sphere  HZEN.  The 
Earth  is  a  point  at  the  centre  of  the  circle.  Some  ob- 
server on  the  Earth  has  a  zenith  Z,  a  nadir  N,  a  horizon 
HR.  P  is  'the  pole  of  the  heavens  and  E  a  point  of  the 
celestial  equator. 

*  Two  lines  drawn  from  the  star  Polaris  to  the  points  L  and  0 
make  an  angle  with  each  other  of  less  than 


LATITUDE.  61 

In  the  figure  PH  measures  the  latitude  of  the  observer, 
because  PH  is  the  north-polar-distance  of  the  north-point 
of  his  horizon.  Z  is  his  zenith,  EZ  is  the  declination  of 
his  zenith  (it  is  the  angular  distance  of  Z  from  the  celestial 
equator). 

Now  the  arc  PH  =  the  arc  EZ  because  the  arc  ZH  is 
90°,  and  PH  =  90°  -  PZ;  moreover,  the  arc  PE  is  90°, 
and  EZ  =  90°  —  PZ.  Therefore  PH  (the  observer's  lati- 
tude) is  measured  by  EZ  (the  decimation  of  his  zenith). 


FIG.  35. 

The  latitude  of  an  observer  is  measured  by  the  declination  of  his  Zenith. 

—  In  Fig.  12  the  latitude  of  the  observer  is  measured  either  by 
(NP)  H  or  by  QZ. 

In  Fig.  16  the  latitude  of  the  observer  is  measured  either  by  the 
angle  PON  or  by  the  angle  COZ  (or  by  the  arcs  PJVand  6YZ). 

In  Fig.  36  the  latitude  of  the  observer  whose  zenith  is  Z  is 
the  elevation  of  the  north  pole  of  the  heavens  (P)  above  his 
horizon  (NWS)  =  40°  ;  it  is  measured  by  the  declination  of  his  zenith 
(Z)  =  40°. 

—  Define  the  latitude  of  an  observer  on  the  Earth  according  to 
Geography.     Define  the   latitude  of  an   observer  on  the  Earth  ac- 
cording to  Astronomy  in  three  ways  :     I.  The  altitude  of  the  North 
Pole  above  the  observer's  horizon  is  the of  the  observer,     II. 


62 


ASTRONOMY. 


The  N.P.D.    of    the    north   point  of  an   observer's  horizon  is  the 

of  the  observer.    III.  The  declination  of  an  observer's  zenith 

is  the of  that  observer. 


FIG.  36. 

So  far  we  have  only  spoken  of  observers  in  the  northern 
hemisphere  of  the  Earth.  The  northern  hemisphere  is 
the  most  important  to  ns,  because  all  the  more  intelligent 
nations  of  the  globe  lived  in  it  for  centuries  and  all  astron- 
omy was  perfected  there.  Later  on,  our  definitions  will 
be  extended  to  cover  all  cases. 

13.  The  Horizon  of  an  Observer  Changes  as  He  Moves 
from  Place  to  place  on  the  Earth. — The  theorem  that  has 
just  been  written  is  easily  proved.  As  the  observer  travels 
from  place  to  place  on  the  Earth  his  zenith  moves  on  the 
celestial  sphere.  It  is  the  point  directly  over  his  head. 


DIURNAL  MOTION  IN  34°  NORTH  LATITUDE.      63 

His  horizon  is  the  plane  always  perpendicular  to  the  line 
joining  his  zenith  and  nadir.  As  this  line  moves  with  the 
motion  of  the  observer  his  horizon  must  move. 

It  is  so  important  to  understand  just  how  the  horizon  of 
an  observer  moves  and  just  how  the  appearances  of  his  sky 
are  changed,  that  it  is  well  worth  while  to  take  space  to 
consider  several  cases. 


FIG.  87. 

The  circles  of  a  celestial  sphere  for  an  observer  in  north  latitude  PJVor  CZ. 

The  student  must  pay  particular  attention  to  this  figure. 

When  he  understands  just  what  it  means  he  has  mas- 
tered all  the  more  important  theorems  of  spherical  astron- 
omy. The  large  circle  stands  for  the  celestial  sphere. 
The  Earth  is  a  point  at  0.  P  is  the  north  pole  of  the 
heavens  (and  p  the  south  pole),  and  hence  D  WCE  must  be 
the  celestial  equator  (since  its  plane  is  perpendicular  to  the 
line  joining  the  poles).  The  celestial  sphere  is  full  of  stars. 


64  ASTRONOMY. 

Now  let  us  suppose  there  is  an  observer  on  the  Earth  ( 0) 
at  some  point  in  the  northern  hemisphere.  If  he  is  in  the 
northern  hemisphere  his  zenith  must  be  somewhere  be- 
tween C  and  P.  Let  us  suppose  that  the  observer  is  on 
the  parallel  of  34°  north  latitude,  say  on  the  parallel  of  Wil- 
mington, N.  C.,  or  of  Los  Angeles,  California.  His  lati- 
tude is  34°  then,  and  his  zenith  must  be  at  Z,  just  34° 
north  of  C.  His  nadir  must  beat  n;  his  horizon  must 
be  N8.  Suppose  that  we  are  looking  at  the  celestial 
sphere,  as  drawn  in  the  figure,  from  a  point  outside  of  it 
and  west  of  it.  W  will  be  his  west  point;  ^his  east  point; 
the  line  EW\&  drawn  so  that  it  looks  (in  perspective)  per- 
pendicular to  NS,  the  observer's  north  and  south  line. 

The  Earth  will  turn  round  once  a  day  on  the  axis  joining 
the  poles  P  and  p.  The  stars  in  the  celestial  sphere  will 
appear  to  rise  above  his  eastern  horizon  NES ;  they  will 
culminate  on  his  meridian  NZS ;  they  will  set  below  his 
western  horizon  NWS.  A  star  which  rises  at  E  will  cul- 
minate at  C  and  set  at  W.  If  he  could  see  below  his  hori- 
zon this  star  would  seem  to  him  to  move  from  W  to  D 
and  then  from  D  to  E  again.  The  interval  of  time  be- 
tween two  successive  risings  would  be  24  hours.  Some 
stars  in  the  north  would  never  set.  All  of  them  would  lie 
within  the  circle  of  perpetual  apparition  KN.  Im  is  the 
diurnal  orbit  of  a  circumpolar  star.  Some  stars  would 
never  rise  to  this  observer.  His  horizon  would  hide  them. 
All  the  stars  further  south  than  the  circle  SR,  (the  circle  of 
perpetual  occultation)  would  never  be  seen.  A  star  near 
the  south  pole  would  have  a  diurnal  orbit  like  or. 

The  student  should  notice  that  a  part  of  this  drawing  is 
quite  independent  of  the  situation  of  the  observer.  We 
can  draw  the  celestial  sphere,  the  celestial  poles,  the  equa- 
tor, the  earth,  and  they  will  be  the  same  for  any  and  every 
observer;  they  will  be  the  same  whether  any  observer  exists 
or  not.  But  the  instant  we  imagine  an  observer  on  the 


DIURNAL  MOTIONS  AT  THE  NORTH  POLE.        65 

earth — anywhere  on  the  earth — his  zenith  is  fixed.  It 
must  be  at  a  point  on  the  celestial  sphere  distant  from  the 
celestial  equator  by  an  arc  equal  to  the  observer's  latitude. 
So  soon  as  the  zenith  is  fixed  a  horizon  is  fixed.  As  soon 
as  the  horizon  is  fixed  we  know  that  some  stars  will  never 
rise  above  it,  and  that  some  stars  will  never  set  below  it. 
If  we  draw  the  celestial  sphere  as  it  is  for  any  particular 
observer  we  shall  be  able  to  say  just  how  the  stars  will  ap- 
pear to  move  for  him;  just  what  stars  he  can  see,  and  just 
what  others  he  can  never  see. 

The  student  should  exercise  himself  in  making  diagrams  of  the 
celestial  sphere  for  observers  in  different  latitudes.  Let  him  make 
such  a  diagram,  placing  the  observer's  zenith  (Z)  at  K  in  the  last 
figure,  and  another  placing  the  observer's  zenith  at  I. 


FIG. 

The  circles  of  the  celestial  sphere  and  the  diurnal  motions  of  the  stars 
as  they  appear  to  an  observer  at  the  north  pole  of  the  earth. 

The  Diurnal  Motion  of  Stars  as  Seen  by  an  Observer  at 
the  North  Pole  of  the  Earth. — An  observer  at  the  north 
pole  of  the  Earth  is  in  terrestrial  latitude  90° ;  the  altitude 
of  the  north  celestial  pole  above  his  horizon  will  be  90°. 


66  ASTRONOMY. 

His  zenith  and  the  north  celestial  pole  will  coincide.  The 
star  Polaris  will  be  neatly  at  his  zenith. 

Fig.  38  shows  the  celestial  sphere  as  it  would  appear 
to  an  observer  at  the  north  pole  of  the  Earth.  The  zenith 
of  the  observer  will  be  exactly  overhead,  of  course,  and 
the  pole  will  coincide  with  his  zenith.  His  horizon  and 
the  celestial  equator  will  coincide,  therefore.  As  all  the 
stars  perform  their  diurnal  revolutions  in  circles  parallel 
to  the  celestial  equator,  no  matter  what  the  latitude,  in  this 
particular  latitude  they  will  revolve  parallel  to  the  horizon. 
None  of  the  stars  of  the  southern  half  of  the  celestial 
sphere  will  be  visible  at  all.  All  the  stars  of  the  northern 
hemisphere  will  be  constantly  visible.  They  will  not  rise 
and  set,  but  they  will  revolve  in  diurnal  orbits  parallel  to 
the  horizon. 

Arctic  explorers  who  travel  from  temperate  regions  to- 
wards the  north  find  the  north  celestial  pole  constantly 
higher  and  higher  above  their  horizon.  When  they  are  in 
latitude  50°,  the  altitude  of  the  pole  (of  the  star  Polaris) 
will  be  50°;  when  they  are  in  latitude  70°,  the  altitude  of 
Polaris  will  be  70°;  if  they  reach  the  pole  of  the  Earth, 
the  altitude  of  Polaris  will  be  90°. 

The  student  may  know  that  from  March  to  September  of  every 
year  the  Sun  is  north  of  the  celestial  equator  (in  north  declination)  ; 
and  that  from  September  to  March  the  Sun  is  south  of  the  celestial 
equator  (in  south  declination).  From  March  to  September,  then, 
the  Sun  is  a  star  of  the  northern  hemisphere  ;  from  September  to 
March  the  Sun  is  a  southern  star.  An  observer  at  the  north  pole 
of  the  Earth  sees  all  the  northern  stars  revolve  in  diurnal  orbits  par- 
allel to  his  horizon,  and  he  will  thus  have  the  Sun  above  the  horizon 
for  six  entire  months,  and  for  the  next  six  months  he  will  not  see 
the  Sun  at  all.  An  observer  at  the  south  pole  of  the  Earth  will 
have  the  Sun  constantly  above  his  horizon  from  September  to 
March;  constantly  below  it  from  March  to  September.  The  Fig.  39 
will  illustrate  the  diurnal  orbit  of  the  Sun  to  an  observer  at  the 
north  pole  of  the  Earth.  The  Sun  is  at  the  point  0  (near  W)  on 
March  22,  and  from  March  to  June  travels  every  day  about  1°  along 


DIURNAL  MOTIONS  AT  THE  EQUATOR. 


67 


the  lowest  broken  line of  the  figure.     The  Sun  is  on  the 

hour  circle  7  on  April  6,  on  77  on  April  22,  on  777  (near  E)  on  May 
8,  on  7  Fon  May  23  (and  always  on  the  dotted  curve).  The  student 
should  trace  out  in  the  picture  the  diurnal  orbits  of  the  Sun  on  the 
dates  just  given. 

The  Diurnal  Motion  of  Stars  as  Seen  by  an  Observer  at 
the  Earth's  Equator. — If  the  observer  is  at  any  point  on 


FIG.  39. 

A  globe  so  set  as  to  show  the  circles  of  the  celestial  sphere  for  an  observer 
at  the  north  pole  of  the  earth. 

the  Earth's  equator  his  terrestrial  latitude  will  be  0° ;  the 
elevation  of  the  north  celestial  pole  above  his  horizon  will 
be  0° ;  the  star  Polaris  will  be  in  his  horizon. 

Fig.  40  shows  the   celestial  sphere  as  it  appears  to  an 


68  A8TRONOMT. 

observer  on  the  Earth's  equator.  The  zenith  of  the  ob- 
server is  in  the  celestial  equator.  The  latitude  of  the  ob- 
server is  0°  and  hence  the  altitude  of  the  north  celestial 
pole  (of  Polaris)  is  0°;  that  is,  the  north  and  south  celes- 
tial poles  are  in  his  horizon.  All  the  stars  appear  to  move 
in  their  diurnal  orbits  parallel  to  the  celestial  equator,  no 
matter  what  may  be  the  observer's  latitude.  In  this  case 
they  will  all  appear  to  revolve  in  circles  perpendicular  to 
the  horizon.  All  the  stars  of  the  sky,  those  in  both  halves 


FIG.  40. 

The  circles  of  the  celestial  sphere  and  the  diurnal  motions  of  the  stars  as 
they  appear  to  an  observer  on  the  earth's  equator. 

of  the  celestial  sphere,  will  be  visible,  for  all  of  them  will 
rise,  every  day,  above  the  eastern  horizon  and  will  pass 
across  the  sky  and  set  below  the  western  horizon.  Every 
star  will  be  above  the  horizon  exactly  half  a  day — 12  hours. 

In  Fig.  41  the  diurnal  paths  of  all  stars  are  perpendicular  to  the 
horizon,  and  every  star  is  12h  above  and  12h  below  it.  Stars  whose 
right-ascension  is  6h  are  on  the  meridian  in  the  picture  The  star  E 
is  3h,  the  stars  A,  B,  are  4h  west  of  the  meridian.  The  vernal  equi- 
nox (0)  is  6h  west. 

The  ecliptic  (the  path  of  the  Sun)  is  marked  on  the  northern  celes- 
tial hemisphere  by  a  broken  line from  0  towards  E, 


DIURNAL  MOTION  OF  TUB  SUN.  69 

etc.  The  Sun  is  at  0  on  March  22  ;  on  the  hour-circle  I,  April  6  ; 
on  II,  April  22  ;  on  III,  May  8;  on  IV,  May  23  (and  always  on  the 
dotted  curve).  The  student  should  trace  out  the  diurnal  orbits  of  the 
Sun  for  the  dates  just  given.  It  is  clear  that  the  Sun  will  cross  the 
celestial  meridian  of  an  observer  at  the  Earth's  equator  north  of  his 
zenith  when  the  Sun  is  in  north  declination  (March  to  September), 
and  south  of  it  whenever  the  Sun  is  in  south  declination  In  our 
latitudes  the  Sun  is  never  seen  north  of  the  zenith,  as  may  be  seen  by 
inspecting  Fig.  33,  where  the  dotted  line  is  the  Sun's  path. 


FIG.  41. 

A  globe  so  set  as  to  show  the  circles  of  the  celestial  sphere  for  an  ob- 
server at  the  earth's  equator.  Z  is  his  zenith  ;  P  the  north  celestial  pole  : 
NWS  his  horizon. 

If  now  the  observer  travels  southward  from  the  equator, 
the  south  pole  will,  in  its  turn,  become  elevated  above  his 
horizon,  and  in  the  southern  hemisphere  appearances  will 
be  reproduced  that  have  been  already  described  for  the 
northern,  except  that  the  direction  of  the  motion  will,  in 


70  ASTRONOMY. 

one  respect,  be  different.  The  heavenly  bodies  will  still 
rise  in  the  east  and  set  in  the  west,  but  those  near  the 
celestial  equator  will  pass  north  of  the  zenith  of  the  ob- 
server instead  of  south  of  it,  as  in  our  latitudes.  The  sun, 
instead  of  moving  from  left  to  right,  there  moves  from 
right  to  left.  In  the  northern  hemisphere  of  the  Earth 
we  have  to  face  to  the  south  to  see  the  sun  ;  while  in  the 
southern  hemisphere  we  have  to  face  to  the  north  to  see  it. 
If  the  observer  travels  west  or  east  on  a  parallel  of  lati- 
tude of  the  Earth's  surface,  his  zenith  will  still  remain  at 
the  same  angular  distance  from  the  north  pole  as  before 
(since  his  terrestrial  latitude  remains  unchanged),  and  as 
the  phenomena  caused  by  the  diurnal  motion  at  any  place 
depend  only  upon  the  altitude  of  the  elevated  pole  at  that 
place,  these  will  not  be  changed  except  as  to  the  times  of 
their  occurrence. 


FIG.  42. 

The  risings  of  the  stars  to  an  observer  on  the  earth  are  earlier  the 
farther  east  he  is.  East  is  in  the  direction  of  the  arrow,  since  the  earth 
revolves  from  west  to  east. 


DIURNAL  MOTIONS  IN  DIFFERENT  LATITUDES.    Tl 

A  star  that  appears  to  pass  through  the  zenith  of  his 
first  station  will  also  appear  to  pass  through  the  zenith  of 
the  second  (since  each  star  remains  at  a  constant  angular 
distance  from  the  pole),  but  later  in  time,  since  it  has  to 
pass  through  the  zenith  of  every  place  between  the  two  sta- 
tions. The  horizons  of  the  two  stations  will  intercept 
different  portions  of  the  celestial  sphere  at  any  one  instant, 
but  the  Earth's  rotation  will  present  the  same  portions  suc- 
cessively, and  in  the  same  order,  at  both.  An  observer  at 
b  (east  of  a)  will  see  the  same  stars  rise  earlier  than  an  ob- 
server at  a.  (See  Fig.  42.) 

Change  of  the  Position  of  the  Zenith  of  an  Observer  by 
the  Diurnal  Motion. — If  the  student  has  mastered  what 
has  gone  before  he  can  solve  any  questions  relating  to  the 
diurnal  motion.  The  following  presentation  of  these  ques- 
tions will  be  found  useful  in  relation  to  problems  of  longi- 
tude and  time,  that  are  to  be  considered  shortly. 

In  Figure  43  nesq  is  the  Earth  ;  NESQ,  is  the  celestial  sphere.  An 
observer  at  n  will  have  his  zenith  at  NP,  and  his  horizon  will  coin- 
cide with  the  celestial  equator.  The  stars  will  appear  to  revolve 
parallel  to  his  horizon  (the  celestial  equator),  as  we  have  seen.  If 
the  observer  is  at  s,  his  zenith  is  at  SP.  If  the  observer  is  in  45° 
north  latitude  (the  latitude  of  Minneapolis),  his  zenith  will  be  at  Z  in 
the  figure.  The  Earth  revolves  on  its  axis  once  daily,  and  the  ob- 
server will  be  carried  round  a  circle.  His  zenith  (Z)  will  move  round 
a  circle  of  the  celestial  sphere  (ML)  corresponding  to  the  parallel  of 
45°  on  the  Earth.  If  the  observer  is  on  the  earth's  equator  at  q,  his 
zenitli  will  be  at  Q,  and  it  will  move  round  the  circle  EQ  of  the  celes- 
tial sphere  once  daily.  If  the  observer  is  at  45°  south  latitude  on 
the  Earth,  his  zenith  will  be  at  S,  and  the  zenith  will  move  round  a 
circle  of  the  celestial  sphere  (SO)  once  daily,  and  so  on.  Thus,  for 
each  parallel  of  latitude  on  the  Earth  we  have  a  corresponding  circle 
on  the  celestial  sphere  (a  parallel  of  declination),  and  each  of  these 
latter  circles  lias  its  poles  at  the  celestial  poles. 

Not  only  are  there  circles  of  the  celestial  sphere  that  correspond 
to  parallels  of  latitude  on  the  Earth,  but  there  are  also  celestial 
meridians  which  correspond  to  the  various  terrestrial  meridians.  The 
plane  of  the  meridian  of  any  place  contains  the  zenith  of  that  place 


72  ASTRONOMY. 

and  the  two  celestial  poles.  It  cuts  from  the  earth's  surface  the  ter- 
restrial meridian,  and  from  the  celestial  sphere  that  great  circle 
which  we  have  defined  as  the  celestial  meridian. 

To  fix  the  ideas,  let  us  suppose  an  observer  at  some  one  point  of  the 
Earth's  surface.  A  north  and  south  line  on  the  Earth  at  that  point 
is  the  visible  representative  of  his  terrestrial  meridian.  A  plane 
through  the  centre  of  the  Earth  and  that  line  contains  his  zenith,  and 


FIG.  43. 

The  change  of  the  position  of  the  observer's  zenith  on  the  celestial  sphere 
due  to  the  diurnal  motion. 


cuts  from  the  celestial  sphere  the  celestial  meridian.  As  the  Earth 
rotates  on  its  axis  his  zenith  moves  round  the  celestial  sphere  in  a  par- 
allel, as  ZL  in  the  last  figure. 

Suppose  that  the  east  point  is  in  front  of  the  picture,  the  west 
point  being  behind  it.  Then  as  the  Earth  rotates  the  zenith  Z  will 
move  along  the  line  ZL  from  Z  towards  L.  The  celestial  meridian 
always  contains  the  celestial  poles  and  the  point  Z,  wherever  it  may 


tilUHNAL  MOTIONS  IN  DIFFERENT  LATITUDES.    73 

be.  Hence,  the  arcs  of  great  circles  joining  N.P.  and  S. P.  in  the  fig- 
ure are  representatives  of  the  celestial  meridian  of  this  observer, 
at  different  times  during  the  period  of  the  Earth's  rotation.  They 
have  been  drawn  to  represent  the  places  of  the  meridian  at  intervals 
of  1  hour.  That  is,  12  of  them  are  drawn  to  represent  12  consecutive 
positions  of  the  meridian  during  a  semi-revolution  of  the  Earth. 

In  this  time  Z  moves  from  Z  to  L.  In  the  next  semi-revolution 
Z  moves  from  L  to  Zt  along  the  other  half  of  the  parallel  ZL.  In  24 
ho  irs  the  zenith  Z  of  the  observer  has  moved  from  Z  to  L  and  from 
L  back  to  Z  again.  The  celestial  meridian  has  also  swept  across  the 
heavens  from  the  position  N  P.,  Z,  Q,  S,  S.P.,  through  every  inter- 
mediate position  to  JV.P.,  L,  E,  0,  S.P ,  and  from  this  last  position 
back  to  N.P.,  Z,  Q,  S,  S.P.  The  terrestrial  meridian  of  the  observer 
has  been  under  it  all  the  time. 

This  real  revolution  of  the  celestial  meridian  is  incessantly  repeated 
with  every  revolution  of  the  Earth.  The  sky  is  studded  with  stars 
all  over  the  sphere.  The  celestial  meridian  of  any  place  approaches 
these  various  stars  from  the  west,  passes  them,  and  leaves  them. 

This  is  the  real  state  of  things.  Apparently  the  observer  is  fixed. 
His  terrestrial  and  celestial  meridians  seem  to  him  to  be  fixed,  not 
only  with  reference  to  himself,  as  they  are,  but  to  be  fixed  in  space. 
The  stars  appear  to  him  to  approach  his  celestial  meridian  from  the 
east,  to  pass  it,  and  to  move  away  from  it  towards  the  west.  When 
a  star  crosses  the  celestial  meridian  it  is  said  to  culminate.  The  pass- 
age of  the  star  across  the  meridian  is  called  the  transit  of  that  star. 
This  phenomenon  takes  place  successively  for  each  observer  on  the 
Earth. 

Suppose  two  observers,  A  and  B,  A  being  one  hour  (15°)  east  of  B 
in  longitude.  This  means  that  the  angular  distance  of  their  terres- 
trial meridians  is  15°  (see  page  28).  From  what  we  have  just  learned 
it  follows  that  their  celestial  meridians  are  also  15°  apart.  When  B's 
meridian  is  N.P.,  Z,  Q,  K,  8.P.,  A's  will  be  the  first  one  (in  the  fig- 
lire)  beyond  it  ;  when  B's  meridian  has  moved  to  this  first  position, 
A's  will  be  in  the  second,  and  so  on,  always  15°  (one  hour)  in  advance. 
A  group  of  stars  that  has  just  come  to  A's  meridian  will  not  pass  B's 
for  an  hour.  When  they  are  on  B's  meridian  they  will  be  one  hour 
west  of  A's,  and  so  on.  A's  zenith  is  always  one  hour  west  of  B's. 
The  same  stars  successively  rise,  culminate,  and  set  to  each  observer 
(A  and  B),  but  the  phenomena  will  be  presented  earlier  to  the  eastern 
observer. 

If  the  student  has  access  to  a  celestial  globe  all  the  prob- 


74  ASTRONOMY. 

lems  that  have  been  considered   in  this  chapter  can  be 
quickly  solved  by  its  use. 

In  Figure  44  Z  is  the  zenith,  .ZVthe  nadir,  and  W  the  west  point 
of  the  observer.  Pis  the  north  celestial  pole,  X,  XI,  .  .  .  XIV,  XV, 
.  .  .  the  celestial  equator.  The  dotted  line  from  P  through  XII  to 
the  south  celestial  pole  is  the  hour-circle  of  12  hours.  The  dotted 
line  inclined  to  the  equator  by  an  angle  of  23°  is  the  sun's  path — the 
ecliptic.  Stars  whose  right-ascension  are  17h  are  on  the  observer's 
celestial  meridian. 

The  star  K  (K.A.  =  13b,  Decl.  =  +  20°)  is  4h  west  of  the  merid- 
ian ;  the  star  R  (R.A.  =  10h,  Decl.  =  -f  30°)  is  just  setting  ;  the 
stars  north  of  Decl.  -(-  50°  are  circumpolar — they  never  set. 

—  Prove  that  as  an  observer  moves  from  place  to  place  his  hori- 
zon must  change.  If  an  observer  is  in  the  northern  hemisphere  of 
the  Earth  his  zenith  is  in  the  northern  half  of  the  celestial  sphere. 
Prove  it  by  a  diagram.  What  is  a  circumpolar  star  ?  Draw  a  dia- 
gram representing  the  celestial  sphere  with  its  poles,  its  equator. 
Now,  suppose  an  observer  on  the  Earth  in  30°  north  latitude ; 
where  will  his  zenith  be  on  the  diagram  ?  Draw  a  circle  to  show 
what  stars  will  always  be  above  his  horizon.  Suppose  an  observer 
in  86°  north  latitude  (the  highest  latitude  reached  by  NANSEN  in 
1895);  where  will  his  zenith  be?  Draw  circles  to  show  how  the 
stars  appeared  to  move  in  their  diurnal  orbits  to  NANSEN.  The  hori- 
zon of  an  observer  in  some  latitude  is  the  same  as  the  celestial  equa- 
tor— in  what  latitude?  An  observer  at  the  north  pole  of  the  Earth 
would  have  the  Sun  constantly  above  his  horizon  for  six  months — 
prove  it.  All  the  stars  are  successively  visible  to  an  observer  on  the 
Earth's*equator — prove  it. 

The  Celestial  Globe. — A  celestial  globe  is  a  globe  marked 
with  the  lines  and  circles  of  the  celestial  sphere — the  celes- 
tial poles,  the  celestial  equator,  the  celestial  meridians  and 
parallels,  etc.,  and  with  the  principal  stars,  each  one  in  its 
proper  right-ascension  and  declination.  The  Figs.  32,  33, 
39,  41,  and  44  represent  such  a  globe  with  the  stars  omit- 
ted. Every  school  should  own  a  celestial  globe,  because  all 
the  problems  of  spherical  astronomy  can  be  simply  ex- 
plained or  illustrated  by  its  use.  In  text-books  we  are 
obliged  to  use  diagrams.  They  are  necessarily  drawn  on  a 


THE  CELESTIAL  GLOBE. 


FIG.  44. 

View  of  a  globe  showing  the  circles  of  the  celestial  sphere  for  an 
observer  in  40°  north  latitude  (the  latitude  of  Philadelphia,  Columbus,  O., 
Quincy,  111.,  Denver,  etc.). 


76  ASTRONOMY. 

flat  surface,  and  the  student  has  to  imagine  the  spherical 
surface.  The  school-globe  shows  the  surface  as  it  really  is. 

The  celestial  globe  must  be  set  so  that  the  elevation  of 
the  north  celestial  pole  (if  the  observer  lives  in  the  north- 
ern hemisphere)  above  the  horizon  is  the  same  as  the  lati- 
tude of  the  observer.  (His  latitude  can  be  taken  from  any 
good  map.)  Then  the  celestial  globe  will  represent  his  ce- 
lestial sphere  just  as  it  really  is,  when  the  line  N8  is  placed 
north  and  south,  N  to  the  north.  Any  one  of  the  problems 
of  this  chapter  can  be  illustrated  by  turning  the  celestial 
globe  about  the  axis.  For  instance,  let  the  student  point 
out  the  circumpolar  stars,  those  that  never  rise  and  set 
to  him.  Let  him  take  a  star  a  little  further  south  and 
turn  the  globe  till  the  star  is  at  the  eastern  horizon — just 
rising.  By  turning  the  globe  slowly  he  will  see  exactly  how 
this  particular  star  moves  in  its  apparent  diurnal  orbit  from 
rising  to  culmination,  and  from  ccilmination  to  setting. 
Let  him  particularly  notice  how  its  altitude  increases  from 
zero  at  rising  to  a  maximum  at  culmination;  and  how  it 
decreases  from  culmination  to  zero  at  setting. 

After  he  has  studied  the  diurnal  motion  of  one  star,  let 
him  choose  another  one  and  trace  its  course  from  rising  to 
setting.  He  should  study,  in  this  way,  the  diurnal  mo- 
tions of  stars  in  all  parts  of  the  sky.  If  he  has  his  globe 
by  him  while  he  is  observing  the  real  stars  in  the  sky,  the 
globe  will  help  him  to  understand  quickly,  in  a  few  min- 
utes, motions  that  the  real  stars  require  24  hours  to  make. 
Other  problems  can  be,  and  should  be,  studied  in  the  same 
way. 


CHAPTER  V. 

CO-ORDINATES -SIDEREAL  AND  SOLAR  TIME. 

14.  Systems  of  Co-ordinates  to  define  the  Place  of  a  Star 
in  the  Celestial  Sphere. — Let  us  now  briefly  consider  some 
of  the  ways  in  which  the  position  of  a  star  in  the  celestial 
sphere  may  be  described.  Many  of  them  are  already  fa- 
miliar. 


FIG.  45.— SYSTEMS  OP  CO-ORDINATES  ON  THE  CELESTIAL  SPHERE. 

Any  great  circles  of  the  celestial  sphere  which  pass 
through  the  two  celestial  poles  are  called  hour -circles. 
Each  hour-circle  is  the  celestial  meridian  of  some  place  on 
the  Earth. 

77 


78  ASTRONOMY. 

The  hour-circle  of  any  particular  star  is  that  one  which 
passes  through  the  star  at  the  time.  As  the  Earth  re- 
volves, different  hour-circles,  or  celestial  meridians,  come 
to  the  star,  pass  over  it,  and  move  away  towards  the  east. 

In  Fig.  45  let  0  be  tlie  position  of  the  Earth  in  the  centre  of  the 
celestial  sphere  NZSD.  Let  Z  be  the  zenith  of  the  observer  at  a 
given  instant,  and  P,  p,  the  celestial  poles.  By  definition  PZSpnNP 
is  his  celestial  meridian.  NS  is  the  horizon  of  the  observer  at  the 
instant  chosen.  PON  is  his  latitude.  If  P  is  the  north  pole,  he  is 
in  latitude  34°  north,  because  the  angle  PON  —  34°. 

ECWD  is  the  celestial  equator  ;  E  and  W  are  the  east  and  west 
points.  The  Earth  is  turning  from  TFto  E.  The  celestial  meridian, 
which  at  the  instant  chosen  in  the  picture  contains  PZp,  was  in  the 
position  PV  about  three  hours  earlier. 

PC,  PB,  PV,  PD  are  parts  of  hour-circles.  If  A  is  a  star,  PB  is 
the  hour-circle  passing  through  that  star.  As  the  Earth  turns  PB 
turns  with  it  (towards  the  east),  and  directly  PB  will  have  moved 
away  from  A  towards  the  top  of  the  picture,  and  soon  the  hour-circle 
PV  will  pass  through  the  star  A.  When  it  does  so,  PV  will  be  the 
hour-circle  of  the  star  A.  At  the  instant  chosen  for  making  the 
picture  PB  is  its  hour-circle. 

We  are  now  seeking  for  ways  of  defining  the  position  of 
a  star,  of  any  star,  on  the  celestial  sphere.  We  define  the 
position  of  a  place  on  the  Earth  by  giving  its  latitude  and 
longitude.  These  two  angles  are  called  the  co-ordinates  of 
this  place.  Co-ordinates  are  angles  which,  taken  together, 
determine  the  position  of  a  point.  If  we  say  that  the 
longitude  of  a  city  is  77°  and  that  its  latitude  is  38°  53'  N., 
we  know  that  this  city  is  Washington.  These  two  num- 
bers determine  its  position.  The  place  of  this  city  is  de- 
scribed by  them  and  no  other  city  can  be  meant. 

To  describe  and  determine  the  place  of  a  star  on  the 
celestial  sphere  we  may  employ  several  different  pairs  of 
co-ordinates.  Those  spoken  of  here  will  all  be  needed  in 
what  is  to  follow. 

North-polar-distance  and  Hour-angle.  —  The  north- 
polar-distance  (N.P.D.)  of  the  star  A  is  PA.  The  hour- 


CELESTIAL   CO-ORDINATES. 


79 


angle  of  a  star  is  the  angular  distance  between  the  celes- 
tial meridian  of  the  observer  and  the  hour-circle  passing 
through  that  star.  The  honr-angle  is  connted  from  the 
meridian  toivards  the  icest  from  0°  to  360°  (or  from  Oh  to 
24b).  The  hoar-angle  of  a  star  at  A  at  the  instant  chosen 
for  making  the  picture  is  ZPB.  The  hour-angle  of  a  star 
at  /iTis  0°.  The  hour-angle  of  a  star  at  Fis  ZPV\  of  a 
star  at  D  is  ZPD  =  180°  =  12h  ;  and  so  on. 

The  hour-angle  is  measured  by  the  arc  of  the  celestial 


45  bis. 


equator  between  the  celestial  meridian  of  the  observer  and 
the  foot  of  the  hour-circle  through  the  star.  The  arc  CB 
is  the  measure  of  the  angle  ZPB.  Knowing  the  two  co- 
ordinates PA  and  CB  the  place  of  the  star  A  is  described 
and  determined. 

North-polar-distance  and  Right-ascension.— The  north- 
polar-distance  of  the  star  A  is  PA,  measured  along  the 
hour-circle  PB.  Let  us  choose  some  fixed  point  F  on  the 


80  ASTRONOMY. 

equator  to  measure  our  other  co-ordinate  from,  and  let  us 
always  measure  it  on  the  equator  towards  the  east  from  0° 
to  360°  (from  Oh  to  24h).  That  is,  from  V  through  B,  <7, 
E,  D,  TF,  successively. 

VB  is  the  right -ascension  of  A.  The  right-ascension  of 
a  star  is  the  angular  distance  of  the  foot  of  the  hour-circle 
through  the  star  from  the  vernal  equinox,  measured  on  the 
celestial  equator,  towards  the  east. 

Exactly  what  the  vernal  equinox  is  we  shall  find  out 
later  on;  for  the  present  it  is  sufficient  to  define  it  as  a 
certain  fixed  point  on  the  celestial  equator.* 

If  we  have  the  right-ascension  and  north-polar-distance 
(K.A.  and  N.P.D.)  of  a  star,  we  can  point  it  out.  Thus 
VB  and  PA  define  the  position  of  A. 

The  right-ascension  of  the  star  A"  is  VC.  Of  a  star  at 
E  it  is  VCE;  of  a  star  at  D  it  is  VCED  ;  of  a  star  at  W  it 
is  VCEDWfwbdi  so  on. 

Right-ascension  and  Declination. — It  is  sometimes  con- 
venient to  use  in  place  of  the  north-polar-distance  of  a  star 
its  declination. 

The  declination  of  a  star  is  its  angular  distance  north  or 
south  of  the  celestial  equator. 

The  declination  of  A  is  BA,  which  is  90°  minus  PA. 

The  relation  between  N.P.D.  and  6  is 

N.P.D.  =  90°  -  tf;    d  =  90°  -  N.P.D. 

North  declinations  are  +  ;  south  declinations  are  — , 
just  as  geographical  latitudes  are  -f  (north)  and  —  (south). 

Altitude  and  Azimuth.— A  vertical  plane  with  respect  to  any  ob- 
server is  a  plane  that  contains  his  vertical  line.  It  must  pass  through 
his  zenith  and  nadir,  and  must  be  perpendicular  to  his  horizon.  A 
vertical  plane  cuts  the  celestial  sphere  in  a  vertical  circle. 


*  It  is,  in  fact,  that  point  at  which  the  Sun  passes  the  celestial 
equator  in  moving  from  the  southern  half  of  the  heavens  to  the 
northern  half.  The  Sun  is  south  of  the  celestial  equator  from  Sep- 
tember 22  to  March  21  and  north  of  it  from  March  21  to  September  22. 


CELESTIAL   CO-ORDINATES. 


81 


FIG.  46. 


As  soon  as  we  imagine  an  observer  to  beat  any  point  on  the  Earth's 
surface  his  horizon  is  at  once  fixed  ;  his  zenith  and  nadir  are  also 

fixed.  From  his  zenith  radiate  a 
number  of  vertical  circles  that 
cut  the  celestial  horizon  perpen- 
dicularly, and  unite  again  at  his 
nadir. 

Some  one  of  these  vertical  cir- 
cles will  pass  through  any  and 
every  star  visible  to  this  observer. 
The  altitude  of  a  heavenly  body 
is  its  angular  elevation  above  the 
plane  of  the  horizon  measured  on 
a  vertical  circle  through  the  star. 

The  zenith  distance  of  a  star  is 
its  angular  distance  from  the 
zenith  measured  on  a  vertical 
circle. 

In  the  figure,  ZS  is  the  zenith  distance  (C)  of  8,  and  HS  (a)  is  its 
altitude.  ZSH  is  an  arc  of  a  vertical  circle. 

ZSH  =  a  +  C  =  90°;  C  =  90°  -  a  ;  a  =  90°  -£. 
The  azimuth  of  a  star  is  the  angular  distance  from  the  point  where 
the  vertical  circle  through  the  star  meets  the  horizon  from  the  north  (or 
south)  point  of  the  horizon.  NHor  SH  is  the  azimuth  of  S  in  Fig. 
46.  The  prime-vertical  of  an  observer  is  that  one  of  his  verti- 
cal circles  that  passes  through  his  east  and  west  points.  The  azi- 
muth of  a  star  on  the  prime- vertical  is  90°. 

Co-ordinates  of  a  Star. — In  what  has  gone  before  we 
have  described  various  ways  of  expressing  the  apparent 
positions  of  stars  on  the  surface  of  the  celestial  sphere. 
That  one  most  commonly  used  in  Astronomy  is  to  give 
the  right-ascension  and  north-polar-distance  (or  declina- 
tion) of  the  star.  The  apparent  position  of  the  star  on  the 
celestial  sphere  is  fixed  by  these  two  co-ordinates  just  as 
the  position  of  a  place  on  the  Earth  is  fixed  by  its  two  co- 
ordinates, latitude  and  longitude. 

If  the  student  has  a  celestial  globe  he  can  set  it  so  as  to  make  the 
preceding  definitions  very  clear.  The  north  pole  of  the  globe  must 
be  above  the  horizon  of  the  globe  by  an  angle  equal  to  the  latitude, 


82  ASTRONOMY. 

In  the  figure  Z  is  the  observer's  zenith,  as  before.  The  star  A  has 
the  following  co-ordinates  :  R.A.  =  2h,  hour-angle  lh  west,  Decl.  = 
+  40°,  N.P.D.  =  50°,  zenith  distance  =  the  arc  ZA,  altitude  =  90° 
—  ZA,  azimuth,  the  arc  measured  on  the  horizon  SWN  from  S 
through  W  to  to  the  foot  of  a  vertical  circle  from  Z  through  A  ; 
the  azimuth  of  A  is  something  more  than  90°.  The  student  should 
point  out  the  corresponding  co-ordinates  for  the  stars  B,  G,  and  D. 


FIG.  47. 

A  globe  showing  the  circles  of  the  celestial  sphere  as  they  appear  to  an 
observer  in  40°  north  latitude. 

Students  mast  try  to  realize  the  circles  that  have  been 
described  in  the  book  as  they  actually  exist  in  the  sky. 
They  are  in  the  sky  first;  and  in  the  book  only  to  explain 
the  appearances  in  the  sky.  On  a  starlit  night  let  him 
first  find  the  north  celestial  pole  (near  the  star  Polaris). 
All  hour-circles  pass  through  this  point.  Next  he  must 


CELESTIAL   CO-ORDINATES.  83 

find  his  zenith.  All  vertical  circles  pass  through  this 
point.  The  great  circle  in  the  sky  that  passes  through  the 
north  pole  of  the  heavens  and  his  own  zenith  is  his  own 
celestial  meridian.  Let  him  trace  it  out  in  the  sky  from 
the  north  point  of  his  horizon  to  the  south  point;  and 
imagine  it  extending  completely  round  the  earth  as  a  great 
circle.  Let  him  choose  a  star  a  little  to  the  west  of  his 
meridian  and  decide  :  1st.  What  is  the  N.P.D.  of  this 
star?  2d.  What  is  its  hour-angle?  Next  he  should  select  a 
star  far  to  the  west,  and  decide  what  its  N.P.D.  and  hour- 
angle  are.  Then  he  should  take  a  star  a  little  to  the  east 
of  his  meridian  and  decide  the  same  points  for  this  star. 
A  little  practice  of  this  sort  will  make  all  the  circles  of  the 
sky  quite  familiar. 

—  Define  hour-circles  of  the  celestial  sphere.  What  is  the  hour- 
circle  of  a  star  ?  Does  a  star  have  different  hour-circles  at  different 
instants  ?  What  are  the  two  co-ordinates  that  determine  the  position 
of  a  point  on  the  surface  of  the  Earth  ?  What  pairs  of  co-ordinates 
may  be  used  to  determine  and  describe  the  position  of  a  star  on  the 
celestial  sphere  ?  Define  the  hour-angle  of  a  star.  What  is  the 
measure  of  the  hour-angle  on  the  celestial  equator  ?  Define  the 
right- ascension  of  a  star.  Hour-angles  are  counted  from  the  celestial 

meridian  of  a  place  towards  the ?     The  right- ascension  of  a  star 

is  counted,  on  the  celestial  equator,  towards  the ? 

15.  Measurement  of  Time ;  Sidereal  Time ;  Solar  Time; 
Mean  Solar  Time — SIDEREAL  TIME. — The  Earth  rotates 
uniformly  on  its  axis  and  it  makes  one  complete  revolution 
in  a  sidereal  day. 

A  sidereal  day  is  the  interval  of  time  required  for  the 
Earth  to  make  one  complete  revolution  on  its  axis,  or,  what 
is  the  same  thing,  it  is  the  interval  between  two  successive 
transits  of  the  same  star  over  the  celestial  meridian  of  a 
place  on  the  Earth.  A  sidereal  day  =  24  sidereal  hours. 
A  sidereal  hour  =  60  sidereal  minutes,  A  sidereal  minute 


84:  ASTRONOMY. 

=  60  sidereal  seconds.     In  a  sidereal  day  the  earth  turns 
through  360°,  so  that 

24  hours  =  360°;  also, 

1  hour  =  15°;  1°  =  4  minutes. 
1  minute  =  15';  1'  =  4  seconds. 
1  second  =  15";  1"  =  0.066  second. 

When  a  star  is  on  the  celestial  meridian  of  any  place  its 
hour-angle  is  zero,  by  definition  (seepage  79).  It  is  then 
at  its  transit  or  culmination. 

As  the  Earth  rotates,  the  meridian  moves  away  (east- 
wardly)  from  this  star,  whose  hour-angle  continually  in- 
creases from  0°  to  360°,  or  from  0  hours  to  24  hours. 
Sidereal  time  can  then  be  directly  measured  by  the  hour- 
angle  of  any  star  in  the  heavens  which  is  on  the  meridian 
at  an  instant  we  agree  to  call  sidereal  0  hours.  When  this 
star  has  an  hour-angle  of  90°,  the  sidereal  time  is  6  hours; 
when  the  star  has  an  hour-angle  of  180°  (and  is  again  on 
the  meridian,  but  invisible  unless  it  is  a  circumpolar  star), 
it  is  12  hours  ;  when  its  hour-angle  is  270°,  the  sidereal 
time  is  18  hours  ;  and,  finally,  when  the  star  reaches  the 
upper  meridian  again,  it  is  24  hours  or  0  hours.  (See  Fig. 
48,  where  ECWD  is  the  apparent  diurnal  path  of  a  star  in 
the  equator.  It  is  on  the  meridian  at  C.) 

Instead  of  choosing  a  star  as  the  determining  point  whose 
transit  marks  sidereal  0  hours,  it  is  found  more  conven- 
ient to  select  that  point  in  the  sky  from  which  the  right 
ascensions  of  stars  are  counted — the  vernal  equinox — the 
point  V  in  Fig.  48.  The  sidereal  time  at  any  instant  is 
measured  ly  the  hour-angle  of  the  vernal  equinox.  The 
fundamental  theorem  of  sidereal  time  is:  TJie  hour-angle 
of  the  vernal  equinox,  or  the  sidereal  time,  is  equal  to  the 
right-ascension  of  the  meridian;  that  is,  CV  —  VC. 

To  avoid  continual  reference  to  the  stars,  we  set  a  clock 
so  that  its  hands  shall  mark  0  hours  0  minutes  0  seconds 


SIDEREAL   TIME.  85 

at  the  instant  the  vernal  equinox  is  on  the  celestial  merid- 
ian of  the  place;  and  the  clock  is  regulated  so  that  exactly 
24  hours  of  its  time  elapses  during  one  revolution  of  the 
Earth  on  its  axis. 

In  this  figure  PZCS  is  the  celestial  meridian  of  the  observer  whose 
zenith  is  Z.  V  is  the  vernal  equinox.  It  is  that  point  on  the  celes- 
tial sphere  from  which  right-ascensions  are  counted.  We  shall  soon 
see  how  to  determine  it. 


PIG.  48. — MEASUREMENT  OF  SIDEREAL  TIME. 

Suppose  that  there  were  a  very  bright  star  exactly  at  V.  (There  is 
no  star  exactly  at  the  vernal  equinox.)  Such  a  star  would  rise  (at  E); 
culminate  (at  C);  and  set  (at  W).  When  it  is  on  the  celestial  merid- 
ian of  the  observer  its  hour-angle  is  Oh  Om  0s  (at  C).  Two  hours 
later  the  star  V  will  have  moved  30°  to  the  westward,  towards  set- 
ting. Its  hour-angle  ZPB  will  then  be  2h.  The  sidereal  time  of  the 
observer  whose  zenith  is  Z  will  then  be  2h.  Six  hours  after  its  cul- 
mination (at  C)  the  star  "Fwill  have  moved  to  TFand  its  hour-angle 
will  be  6h.  The  sidereal  time  of  the  particular  observer  whose  zenith 


86  ASTRONOMY. 

is  Z  will  then  be  6h.  When  Fhas  moved  to  Z>,  the  sidereal  time  will 
be  12h.  When  F  has  moved  to  E,  the  sidereal  time  will  be  18h. 
When  V  has  moved  to  C  the  sidereal  time  will  be  241'  (or  O'1  again) 
and  a  new  sidereal  day  will  begin  ;  and  so  on  forever. 

When  the  hour-angle  of  V  is  2h  and  the  vernal  equinox 
is  at  It,  the  right-ascension  of  the  celestial  meridian  (of  the 


FIG.  49. 

The  hour-angle  of  the  vernal  equinox,  O,  in  this  figure  is  2  hours  west. 
The  sidereal  time  is  therefore  2  hours.  The  R.A.  of  the  observer's  merid- 
ian is  2  hours. 

point  (7)  is  2h.  The  right-ascension  of  any  star  on  the 
meridian  at  that  instant  must  be  2  hours.  Speaking  gen- 
erally, when  the  vernal  equinox  is  anywhere  (as  at  F  in 
Fig.  48)  the  right-ascension  of  the  celestial  meridian  (of  the 
point  C)  in  the  figure  will  be  VC.  The  sidereal  time  is 
the  angle  ZP  V  measured  by  the  arc  CV.  The  right-ascen- 


SIDEREAL  TIME.  87 

sion  of  the  meridian  is  VC.     The  right-ascension  of  any 
star  on  the  meridian  at  that  instant  will  be  VC. 

Conversely — if  a  star  C  is  on  the  celestial  meridian  of  a 
place  at  any  instant  the  right-ascension  of  that  star  is  ex- 
pressed by  the  same  number  of  degrees  (or  of  hours)  as  the 
hour-angle  of  the  vernal  equinox  or  as  the  sidereal  time. 


FIG.  50. 

The  hour-angle  of  the  vernal  equinox,  O,  in  this  figure  is  3  hours  west. 
The  sidereal  time  is  therefore  3  hours.  The  R.  A.  of  the  observer's  merid- 
ian is  3  hours. 

Suppose  then  that  we  had  a  catalogue  of  the  right-ascensions  of 
stars  like  this — and  we  have  such  catalogues.  See  Table  V  for  a 
specimen  of  the  sort : 

The  R.  A.  of  the  star  Aldebaran  is    4h  30"' 
"     "     ""    "     "    Siriusis  6h  41m 

"     "     "    "    "     "     Regulm\s      10h    3m 
"     "     "    "    "     "     Spica  is  13h  20m 

*'     "     "    "    "     "     Arcturus  is     14h  llm 
"     "     "    "    "     "     Vega  is  18h  34m 

"     "     "    "    "     "     Fomalhaut  is  22b  52m 


88  ASTRONOMY. 

Suppose  further  that  we  Lad  a  way  of  knowing  when  a  star  was 
on  our  celestial  meridian,  that  is,  exactly  south  of  us  (and  we  have 
such  a  way,  as  will  soon  be  seen),  then  if  an  observer  noticed  that 
Sirius  was  on  his  celestial  meridian  at  a  certain  instant  he  would  know 
that  the  sidereal  time  at  that  instant  must  be  6h  411*1.  (For  the  R.A. 
of  Sirius  is  6'1  41ra  and  this  is  the  R.A.  of  the  meridian,  and  this  is 
equal  to  the  hour-angle  of  the  vernal  equinox;  and,  finally,  this  is 


FIG.  51. 

The  hour-angle  of  the  vernal  equinox,  O,  in  this  figure  is  6  hours  west. 
The  sidereal  time  is  therefore  6  hours.  The  R.A  of  the  observer's  merid- 
ian is  6  hours. 

the  sidereal  time  at  that  instant).  If  the  star  FomalJiavt  is  on  the 
celestial  meridian  of  an  observer  at  another  instant,  the  sidereal  time 
at  that  instant  must  be  22h  52m,  and  so  on.  The  sidereal  clock  must 
show  on  its  dial  61'  41ni  when  Sirius  is  on  the  meridian  ;  and  it  must 
show  22h  52m  when  Fomalhaut  is  on  the  meridian,  and  so  on.  As 
soon  as  we  know  the  right-ascension  of  one  star  we  can  set  the  hands 
of  the  sidereal  clock  correctly.  When  Sirius  is  on  the  meridian  on 


8IDERIAL  TIME. 


89 


FIG.  52. 

The  hour-angle  of  the  vernal  equinox  in  this  figure  is  17  hours.  The 
sidereal  time  is  therefore  17  hours.  The  R.A.  of  the  observer's  meridian 
is  17  hours. 


90  ASTRONOMY. 

Monday  they  must  point  to  6h  41m.  When  Sinus  comes  to  the  merid- 
ian on  Tuesday  they  must  again  mark  61'  41m.  And  it  is  just  the 
same  for  other  stars.  Any  star  whose  right-ascension  is  known  will 
enable  us  to  set  the  hands  of  the  sidereal  clock  correctly  as  soon  as 
we  know  the  direction  of  our  meridian  in  space.  The  hour-hand  of 
the  clock  must  move  over  24h  every  day,  from  one  transit  of  the  star 
till  the  next  succeeding  transit. 

Solar  Time. — Time  measured  by  the  hour-angle  of  the 
sun  is  called  true  (or  apparent)  solar  time.  An  apparent 
solar  day  is  the  interval  of  time  between  two  consecutive 
transits  of  the  Sun  over  the  celestial  meridian.  The  instant 
of  the  transit  of  the  Sun  over  the  meridian  of  any  place  is 
the  apparent  noon  of  that  place,  or  local  apparent  noon. 

When  the  Sun's  hour-angle  is  12  hours  or  180°,  it  is  lo- 
cal apparent  midnight. 

The  ordinary  sun-dial  marks  apparent  solar  time.  As  a 
matter  of  fact,  apparent  solar  days  are  not  equal.  In  in- 
tervals of  time  that  are  really  equal  the  hour-angle  of  the 
true  Sun  changes  by  quantities  that  are  not  quite  equal. 
The  reason  for  this  will  be  fully  explained  later.  Hence 
our  clocks  are  not  made  to  keep  this  kind  of  time. 

Mean  Solar  Time. — A  modified  kind  of  solar  time  is 
therefore  used,  called  mean  solar  time.  This  is  the  time 
kept  by  ordinary  watches  and  clocks.  It  is  sometimes 
called  civil  time,  because  it  regulates  our  civil  affairs. 
Mean  solar  time  is  measured  by  the  hour-angle  of  the  mean 
Sun,  a  fictitious  body  which  is  imagined  to  move  uniformly 
in  the  equator.  We  have  tables  that  give  us  the  position 
of  this  imaginary  body  at  any  and  every  instant,  just  as  cat- 
alogues of  stars  give  us  the  right-ascensions  of  stars.  We 
may  therefore  speak  of  the  transit  of  the  mean  Sun  as  if 
it  were  a  bright  shining  point  in  the  sky.  A  mean  solar 
day  is  the  interval  of  time  between  two  consecutive  transits 
of  the  mean  Sun  over  the  celestial  meridian.  Mean  noon  at 
any  place  is  the  instant  when  the  mean  Sun  is  on  the  ce- 


MEAN  SOLAR  TIME.  91 

lestial  meridian  of  that  place  (at  C  in  Fig.  48).  Twelve 
hours  after  local  mean  noon  is  local  mean  midnight.  The 
mean  sun  is  then  at  D  in  Fig.  48.  The  mean  solar  day  is 
divided  into  24  hours  of  60  minutes  each. 

Astronomers  begin  the  mean  solar  day  at  noon  and  count 
round  to  24  hours.  It  happens  to  be  convenient  for  them 
to  do  so.  In  ordinary  life  the  civil  day  is  supposed  to  be- 
gin at  midnight,  and  is  divided  into  two  periods  of  12 
hours  each.  When  the  mean  Sun  is  at  Z),  in  Fig. 
48,  it  is  midnight  (12h)  of  Sunday — Monday  begins. 
When  the  mean  Sun  is  at  6",  it  is  mean  noon  (12h)  of  Mon- 
day. When  the  mean  Sun  has  again  reached  D  it  is  mid- 
night (12h) — Tuesday  begins,  and  so  on.  It  is  more  con- 
venient, in  ordinary  life,  to  change  the  date — the  day — at 
midnight,  when  most  persons  are  asleep. 

Everything  that  is  here  said  about  the  measurement  of  time  can  be 
clearly  illustrated  by  the  use  of  a  celestial  globe.  Set  the  globe  to 
correspond  to  the  observer's  latitude.  The  vernal  equinox  is  marked 
on  every  globe.  Place  the  vernal  equinox  on  the  meridian  of  the  ob- 
server. It  is  now  sidereal  Oh.  Rotate  the  globe  slowly  to  the  west. 
The  hour  angle  of  the  vernal  equinox  measures  the  sidereal  time. 
Trace  the  course  of  the  equinox  throughout  a  whole  revolution  ;  that 
is,  throughout  a  sidereal  day. 

Again,  suppose  the  sun  to  be  in  north  declination  15°,  and  in  R.  A.  2h 
3im  (its  approximate  position  on  May  1  of  each  year).  Find  this  point 
on  the  globe  (see  Fig.  50),  and  trace  the  sun's  course  from  rising  to 
setting,  and  to  rising  again  ;  that  is,  throughout  24h.  You  will  see 
that  the  sun  rises  north  of  the  east  point  on  May  1  and  reaches  a  high 
altitude  at  noon  for  observers  in  the  northern  hemisphere  of  the 
Earth. 

Again,  suppose  the  Sun  to  be  in  south  declination  15°,  and  in  R.  A. 
14h  34m,  its  approximate  position  on  November  3  of  each  year  (see 
Fig.  52).  Find  this  point  on  the  globe,  and  trace  the  Sun's 
course  from  rising  to  setting,  and  to  rising  again.  You  will  see  that 
the  Sun  rises  south  of  the  east  point  on  November  3,  and  that  its  alti- 
tude at  noon  is  considerably  less  in  November  than  in  May. 

The  student  should  also  try  to  realize  all  these  explana- 


92  ASTRONOMY. 

tions  regarding  time  by  conceiving  the  appearances  in  the 
sky.  On  a  starlit  night  he  should  face  southwards  and  he 
will  see  some  star  on  his  celestial  meridian.  If  the  right 
ascension  of  that  star  is  3h  24m  16.93s  then,  at  that  instant, 
the  sidereal  time  is  3h  24m  16.93s;  a  second  later  it  is  3h 
24m  17.93s;  an  hour  later  still  it  is  4h  24m  17.93%  and  so 
on.  Let  him  trace  out  in  the  sky  the  position  of  the  ce- 
lestial equator.  The  vernal  equinox  must  be  west  of  his 
meridian  by  an  arc  of  3b  24m,  etc.,  or  of  51°.  Let  him 
fix  in  his  mind  a  point  of  the  equator  51°  west  of  the  me- 
ridian. The  vernal  equinox  is  there.  In  an  hour  it  will 
be  15°  further  to  the  west;  in  two  hours  it  will  be  30°  far- 
ther, and  so  on.  In  24  hours  it  will  have  made  the  circuit 
of  the  sky  and  have  returned  to  its  former  place  once  more. 
The  same  kind  of  exercises  should  be  gone  through  with 
in  the  daytime,  so  as  to  realize  the  motions  of  the  mean 
Sun.  The  mean  Sun  is  never  very  far  away  from  the  true 
Sun.  At  noon  the  Sun  is  due  south,  on  the  celestial  me- 
ridian. At  2  P.M.  the  hour-angle  of  the  mean  Sun  is  21' ; 
at  3  P.M.  it  is  3h;  at  midnight  it  is  12h. 

—  Define  a  sidereal  day.  What  is  the  measure  of  the  sidereal  time 
at  any  instant?  When  the  vernal  equinox  is  on  the  celestial  merid- 
ian of  a  place,  what  is  the  sidereal  time  at  that  instant  ?  What  is  the 
relation  between  the  sidereal  time  at  any  instant  and  the  right  ascen- 
sion of  the  meridian  at  that  instant  ?  Draw  a  diagram  that  will  show 
that  relation.  If  a  star  whose  R.A.  is  6h  41m  is  on  the  celestial  merid- 
ian of  a  place  at  a  certain  instant,  what  is  the  sidereal  time  of  that 
place  at  that  instant  ?  If  you  knew  that  the  R  A.  of  Siriiis  was  61' 
4  lm,  how  could  you  set  the  hands  of  a  clock  so  as  to  mark  the  correct 
sidereal  time?  What  is  true  solar  time?  What  kind  of  time  is  marked 
by  a  sun-dial?  How  is  mean  solar  time  measured?  Is  the  mean 
Sun  a  body  that  really  exists  ?  Is  there  any  objection  to  imagining 
such  a  body  to  exist  in  the  sky,  and  to  supposing  that  it  has  motions 
from  rising  and  setting  like  the  stars?  What  is  a  mean  solar  day? 
Define  the  instant  of  mean  noon.  How  many  hours  in  a  mean  solar 

day  ?     In  civil  life  we  divide  a  mean  solar  day  into groups  of 

hours  each.     If  you  have  a  celestial  globe  use  it  so  as  to  illus- 


TIME.  93 

trate  what  you  have  learned  about  different  kinds  of  time.  Stand  up 
and  imagine  yourself  out  of  doors  on  a  starlit  night.  Point  at  your 
zenith  (Z).  Point  out  your  horizon.  Point  out  the  north  celestial 
pole  (P)  (it  is  at  an  altitude  equal  to  your  latitude).  Point  out 
the  celestial  equator.  Choose  some  point  of  the  equator  to  be  the 
vernal  equinox  V.  What  is  the  hour-angle  of  F  ?  (Answer  :  It  is 
ZP  V — point  out  this  angle.)  lu  an  hour  from  now  where  will  Fbe? 
in  two  hours?  in  24  hours  ?  Why  does  F  have  different  positions 
in  the  sky  at  different  instants  ?  In  speaking  of  sidereal  time  we 
refer  everything  to  V=  the  vernal  equinox.  Now,  suppose  that  in- 
stead of  considering  the  motions  of  Fjou  think  of  the  motions  of  the 
true  Sun.  Describe  those  motions  as  well  as  you  know  them,  and  say 
what  the  apparent  solar  time  is.  Do  the  same  things  for  the  mean 
Sun.  Do  you  now  thoroughly  understand  that  the  hour-angle  of  the 
mean  Sun  is  measured  by  the  motion  of  the  hour-hand  of  your  watch? 
The  hands  of  your  watch  point  to  4  P.M.  What  event  took  place  4 
hours  ago  (supposing  your  watcu  to  be  keeping  local  mean  solar 
time)? 


CHAPTER  VI. 

TIME— LONGITITUDE. 

16.  Time — Terrestrial  Longitudes. — We  have  seen  that 
time  may  be  reckoned  in  at  least  three  ways.  The  natural 
unit  of  time  is  the  day. 

A  sidereal  day  is  the  time  required  for  the  Earth  to  turn 
once  on  its  axis;  it  is  measured  by  the  interval  between 
two  successive  transits  of  the  same  star  (sidereus  is  the 
Latin  for  a  star  or  a  group  of  stars)  over  the  same  celestial 
meridian. 

A  solar  day  is  the  interval  of  time  between  two  succes- 
sive transits  of  the  true  Sun  over  the  same  celestial  merid- 
ian. It  is  longer  than  a  sidereal  day,  because -the  Sun  ap- 
pears to  be  constantly  moving  eastwards  among  the  stars 
(as  we  shall  soon  see),  so  that  if  the  Sun  has  the  same 
right-ascension  as  the  star  Sirius  on  Monday  noon,  by 

«-o         «-o 

East  West 

#  * 

Monday  Tuesday 

Tuesday  noon  it  will  have  moved  about  a  degree  to  the 
east  of  Sirius.  Therefore  Sirius  will  come  to  the  celes- 
tial meridian  on  Tuesday  a  little  earlier  than  the  Sun,  and 
hence  the  solar  day  will  be  a  little  longer  than  the  sidereal 
day.  The  eastward  motion  of  the  true  Sun  in  right- 
ascension  is  not  uniform,  so  that  intervals  of  time  that  are 
really  equal  are  not  measured  by  equal  angular  motions  of 
the  true  Sun.  The  true  Sun  moves  in  the  ecliptic — not 
in  the  celestial  equator.  Hence  a  "  mean  Sun  "  has  been 

94 


TIME.  95 

invented,  as  it  were.  The  mean  Sun  is  an  imaginary 
point — like  a  star — moving  uniformly  along  the  celestial 
equator  so  as  to  make  one  complete  circuit  of  the  heavens  in 
a  year. 

A  mean  solar  day  is  the  interval  of  time  between  two 
successive  transits  of  the  mean  Sun  over  the  same  celestial 
meridian.  As  the  mean  Sun  moves  eastwards  among  the 
stars,  a  mean  solar  day  is  longer  than  a  sidereal  day.  The 
exact  relation  is: 

1  sidereal  day  =  0.997  mean  solar  day,# 

24  sidereal  hours  =  23h  56m  4". 091  mean  solar  time, 

1  mean  solar  day  =  1.003  sidereal  days, 

24  mean  solar  hours  =  24h  3m  56s. 555  sidereal  time, 

and 

366.24222  sidereal  days  =  365.24222  mean  solar  days. 

Local  Time. — When  the  mean  Sun  is  on  the  celestial 
meridian  of  any  place,  as  Boston,  it  is  mean  noon  at  Bos- 
ton. When  the  mean  Sun  is  on  the  celestial  meridian  of 
St.  Louis,  it  is  mean  noon  at  St.  Louis.  St.  Louis  being 
west  of  Boston,  and  the  Earth  rotating  from  west  to  east, 
the  local  noon  of  Boston  occurs  earlier  than  the  local  noon 
at  St.  Louis.  The  local  sidereal  time  at  Boston  at  any 
given  instant  is  expressed  by  a  larger  number  than  the  local 
sidereal  time  of  St.  Louis  at  that  instant. 

The  sidereal  time  of  mean  noon  can  be  calculated  before- 
hand (as  we  shall  see)  and  is  given  in  the  astronomical 
ephemeris  (the  Nautical  Almanac,  so  called)  for  every  day 
of  the  year.  We  can  thus  determine  the  local  mean  solar 
time  when  we  know  the  sidereal  time.  In  what  precedes 
we  have  shown  (page  84)  how  to  set  and  regulate  a  sidereal 
clock.  A  mean-solar  clock  can  be  regulated  by  comparing 
it  with  a  sidereal  time-piece  as  well  as  by  direct  observa- 
tion of  the  Sun.  After  the  student  understands  the  con- 
struction and  use  of  astronomical  instruments  we  shall  re- 


96  ASTRONOMY. 

turn  to  this  matter  of  time  and  show  exactly  how  the  mean 
solar  time  of  our  clocks  and  watches  is  determined. 

Terrestrial  Longitudes. — Owing  to  the  rotation  of  the 
Earth,  there  is  no  such  fixed  correspondence  between  merid- 
ians on  the  Earth  and  meridians  on  the  celestial  sphere  as 
there  is  between  latitude  on  the  Earth  and  declination  in 
the  heavens.  The  observer  can  always  determine  his  lati- 
tude by  finding  the  declination  of  his  zenith,  but  he  can- 
not find  his  longitude  from  the  right-ascension  of  his 
zenith  with  the  same  facility,  because  that  right-ascension 
is  constantly  changing. 

Consider  the  plane  of  the  meridian  of  a  place  extended 
out  to  the  celestial  sphere  so  as  to  mark  out  on  the  latter 
the  celestial  meridian  of  the  place.  Take  two  such  places, 
Washington  and  San  Francisco,  for  example;  then  there 
will  be  two  such  celestial  meridians  cutting  the  celestial 
sphere  so  as  to  make  an  angle  of  about  forty-five  degrees 
with  each  other  in  this  case. 

Let  the  observer  imagine  himself  at  San  Francisco.  His 
celestial  meridian  is  over  his  head,  at  rest  with  reference  to 
him,  though  it  is  moving  among  the  stars.  Let  him  con- 
ceive the  meridian  of  Washington  to  be  visible  on  the 
celestial  sphere,  and  to  extend  from  the  pole  over  toward 
his  southeast  horizon  so  as  to  pass  about  forty-five  degrees 
east  of  his  own  meridian.  It  would  appear  to  him  to  be  at 
rest,  although  really  both  his  own  meridian  and  that  of  Wash- 
ington are  moving  in  consequence  of  the  Earth's  rotation. 

The  stars  in  their  courses  will  first  pass  the  meridian  of 
Washington,  and  about  three  hours  later  they  will  pass  his 
own  meridian.  Kow  it  is  evident  that  if  he  can  determine 
the  interval  which  a  star  requires  to  pass  from  the  merid- 
ian of  Washington  to  that  of  his  own  place,  he  will  at 
once  have  the  difference  of  longitude  of  the  two  places  by 
turning  the  interval  of  time  into  degrees,  at  the  rate  of  35° 
to  each  hour. 


LONGITUDE. 


97 


The  difference  of  longitude  between  any  two  places  depends  upon 
tlie  angular  distance  of  the  terrestrial  (or  celestial)  meridians  of 
these  two  places,  and  not  upon  the  motion  of  the  star  or  sun  which 
is  used  to  determine  this  angular  difference,  and  hence  thejongitude 
of  a  place  is  the  same  whether  expressed  as  the  difference  of  two 
sidereal  or  of  two  solar  times.  The  longitude  of  Washington  west 
from  Gfreenwich  is  5h  8ra  or  77°,  and  this  is  in  fact  the  ratio  of  the 
angular  distance  of  the  meridian  of  Washington  from  that  of  Green- 
wich, to  24  hours  or  360°.  The  angle  between  the  two  meridians  is 
of  24  hours,  or  of  a  whole  circumference. 


FIG.  53.— RELATION  BETWEEN  TERRESTRIAL  MERIDIANS  AND 
CELESTIAL  MERIDIANS. 

Every  observer  on  the  earth  has  a  terrestrial  meridian  on  which  he 
stands  and  a  celestial  meridian  over  his  head.  The  latter  passes  through 
the  celestial  poles  and  the  observer's  zenith. 

The  difference  of  longitude  of  any  two  places  on  the  Earth 
is  measured  ly  the  difference  of  their  simultaneous  local 
times, 


98  ASTRONOMY. 

If  two  stations  on  the  Earth  (say  Greenwich  and  Wash- 
ington) have  sidereal  time-pieces  set  and  regulated  properly 
to  the  two  local  times,  we  shall  know  the  difference  of 
longitude  of  the  two  places  as  soon  as  we  can  compare  the 
two  time-pieces.  The  dials  will  differ  by  the  difference  of 
longitude. 

One  way  to  determine  the  longitude  is  actually  to  carry 
the  Washington  time-piece  over  to  Greenwich  and  to  com- 
pare its  dial  with  that  of  the  Greenwich  time-piece.  When 
the  Greenwich  time-piece  marks  5h  8m  P.M.  the  Washing- 
ton time-piece  will  mark  Oh  (noon).  We  cannot  transport 
pendulum  clocks  by  sea  and  keep  them  running,  so  that 
the  Washington  time-piece  referred  to  must  be  a  chro- 
nometer, which  is  nothing  but  a  large  and  perfect  watch 
kept  going  by  the  motive  power  of  a  coiled  spring. 

A  much  better  way  of  comparing  the  two  time-pieces  is 
to  send  the  beats  of  a  clock  by  telegraph  from  one  station 
to  the  other.  It  is  possible  to  arrange  things  so  that  an 
observer  at  Greenwich  can  make  a  signal  that  can  be  ob- 
served at  Washington.  If  Greenwich  sends  a  signal  at 
5h  8m  P.M.,  Washington  will  note  the  face  of  the  standard 
clock  when  it  is  received,  and  the  Washington  local  time 
will  be  Oh  (noon).  A  Greenwich  signal  sent  at  6h  8m  local 
Greenwich  time,  will  be  received  at  Washington  at  lh,  and 
so  on.  This  is  the  theory  of  the  method  now  universally 
employed  for  exact  determinations  of  longitude.  It  was 
first  employed  by  oar  Coast  and  Geodetic  Survey  between 
Baltimore  and  Washington  in  1844,  and  it  was  called  "  the 
American  method." 

It  is  of  vital  importance  to  seamen  to  be  able  to  deter- 
mine the  longitude  of  their  vessels.  The  voyage  between 
Liverpool  and  New  York  is  made  weekly  by  scores  of 
steamers,  and  the  safety  of  the  voyage  depends  upon  the 
certainty  with  which  the  captain  can  mark  the  longitude 
and  latitude  of  his  vessel  upon  the  chart. 


LONGITUDES  AT  SEA.  99 

The  method  used  by  a  sailor  is  this:  with  a  sextant  (see 
Chapter  VII)  the  local  time  of  the  ship's  position  is  de- 
termined by  an  observation  of  the  Sun.  That  is,  on  a 
given  day  he  can  set  his  watch  so  that  its  hands  point  to 
twelve  at  local  mean  noon.  He  carries  on  his  ship  a 
chronometer  which  is  regulated  to  Greenwich  mean  time. 
Its  hands  always  point  to  the  Greenwich  hour,  minute,  and 
second.  Suppose  that  when  the  ship's  time  is  Oh  (noon) 
the  Greenwich  time  is  3h  20m.  The  ship  is  west  of  Green- 
wich 3h  20m  —  50°.  The  difference  of  simultaneous  local 
times  measures  the  difference  of  longitude.  '  Hence  the 
ship  is  somewhere  on  the  terrestrial  meridian  of  50°  west  of 
Greenwich.  If  the  altitude  of  the  pole-star  is  measured, 
the  latitude  of  the  ship  is  also  known.  Suppose  the  alti- 
tude of  the  pole-star  above  the  horizon  to  be  45°.  The 
ship  is  then  in  the  regular  track  of  vessels  bound  for  Liver- 
pool. Observations  like  this  are  made  every  day. 

When  the  steamer  Faraday  was  laying  the  direct  cable  from 
Europe  to  America  she  obtained  her  longitude  every  day  by  compar- 
ing her  ship's  time  (found  by  observation  on  board)  with  the  Green- 
wich time  telegraphed  along  the  cable  and  received  at  the  end  of  it 
which  she  had  on  her  deck. 

From  the  National  Observatory  at  Washington  the  beats  of  a  clock 
are  sent  out  by  telegraph  along  the  lines  of  railway  every  day  at 
Washington  noon  ;  at  every  railway  station  and  telegraph  office  the 
telegraph  sounder  beats  the  seconds  of  the  Washington  clock.  Any 
one  who  can  set  his  watch  to  the  local  time  of  his  station  (by  making 
observations  of  the  sun  at  his  own  station),  and  who  can  compare  it 
with  the  signals  of  the  Washington  clock,  can  determine  for  himself 
the  difference  of  the  simultaneous  local  times  of  Washington  and  of 
his  station,  and  thus  his  own  longitude  east  or  west  from  Wash- 
ington. 

Standard  Time  in  the  United  States. — In  a  country  of 
small  area,  it  is  practicable  to  use  the  local  time  of  its  cap- 
ital city  all  over  the  country.  Greenwich  time  (nearly  the 
same  as  London  time)  is  the  standard  time  of  the  whole  of 


100  ASTRONOMY. 

England.  The  case  is  not  quite  the  same  in  a  country  of 
wide  extent  in  longitude.  San  Francisco  is  about  3h  west 
of  Washington,  and  it  would  be  inconvenient  to  use  Wash- 
ington local  time  in  San  Francisco. 

The  matter  was  regulated  in  1883  by  the  railways  of  the 
United  States  and  Canada,  which  adopted  the  system  now 
in  use.  By  this  system  the  continent  was  divided  into 
four  sections,  each  15°  (one  hour)  of  longitude  in  width 
(from  east  to  west).  Each  section  extended  south  from 
the  Arctic  Ocean  to  Central  America  and  the  Gulf.  In 
each  section  a  central  meridian  was  chosen,  and  the  local 
time  of  that  meridian  was  taken  for  the  standard  time  of 
all  the  cities  and  towns  of  that  section.  The  meridians 
chosen  as  central  were: 

I.  The  meridian  of  75°  W.  from  Greenwich  (it  passes 
west  of  Albany  and  east  of  Philadelphia). 

II.  The  meridian  of  90°  W.  from  Greenwich  (it  passes 
east  of  St.  Louis  and  nearly  through  New  Orleans). 

III.  The  meridian  of  105°  W.  from  Greenwich  (it  passes 
a  little  to  the  west  of  Denver). 

IV.  The  meridian  of  120°  W.  from  Greenwich  (it  passes 
a  little  west  of  Virginia  City  and  of  Santa  Barbara). 

The  local  time  of  the    75th  meridian  was  called  Eastern  Time  ; 
"       "        "     "     "    90th  "  "         "     Central  Time; 

"       •«        "     "     "105th  "  "         "     Mountain  Time ; 

"     "     "  120th  "  "         "     Pacific  Time. 

Greenwich  time  is  5  hours  later  than  Eastern  time  ; 
"  "     "  6     "         "         "     Central  time ; 

"  "     "  7     "         "         "     Mountain  time; 

"  «     ««  g     ««         ««         «     Pacific  time. 

Eastern  lime  is  used  throughout  the  New  England  States,  Pennsyl- 
vania, New  Jersey,  Delaware,  the  Virginias,  and  in  the  greater  por- 
tion of  the  Carolinas  east  of  the  Blue  Ridge. 

Central  time  is  used  in  Florida  and  Georgia  and  in  the  Central 
States,  including  Texas,  most  of  Kansas  and  Nebraska,  and  in  the 
half  of  the  two 


STANDARD  TIME.    '  101" 

Mountain  time  is  used  in  the  group  of  States  about  the  Rocky 
Mountains,  including  most  of  Arizona,  Utah,  Idaho,  and  Montana. 
Pacific  time  is  used  in  the  Pacific  States. 

Throughout  the  United  States  and  Canada  every  watch 
and  clock  running  on  standard  time  should  show  the  same 
minute  and  second.  The  hour  hands  alone  should  differ. 
Standard  time  is  Greenwich  time,  so  far  as  the  minutes 
and  seconds  are  concerned,  with  an  arbitrary  change  of 
whole  hours  in  the  different  sections.  All  time-pieces  in 
England  show  Greenwich  time.  The  chronometers  of  most 
ships  on  the  Atlantic  run  on  Greenwich  time.  All  time- 
pieces in  the  United  States  run  on  Greenwich  time  so  far 
as  the  minutes  and  seconds  are  concerned ;  the  only  differ- 
ence is  a  difference  in  the  whole  hour.  The  chronometers 
of  most  ships  in  the  Pacific  Ocean  run  on  Greenwich  time, 
with  no  change  in  the  hour. 

The  standard  time  of  the  Hawaiian  Islands  will  probably  be  that 
of  the  150th  meridian  west  of  Greenwich  (10  hours  slower  than 
Greenwich  time);  that  of  the  Philippine  Islands  will  probably  be  the 
local  time  of  the  120th  meridian  east  of  Greenwich  (8  hours  faster 
than  Greenwich  time).  Cape  Colony  (Cape  of  Good  Hope)  time  is 
lh  30™  fast  of  Greenwich  time,  and  Natal  time  is  2h  fast  The  time 
of  West  Australia  is  8h,  of  Japan  and  South  Australia  9h,  of  Victoria 
and  Queensland  10h,  and  of  New  Zealand  llh  30m  fast  of  Greenwich 
time.  On  the  Continent  of  Europe,  Belgium  and  Holland  use  Green- 
wich time  unchanged,  while  Norway,  Sweden,  Denmark,  Austria, 
and  Italy  employ  a  standard  time  lh  fast  of  Greenwich  time.  France 
still  holds  to  the  meridian  of  Paris  as  standard,  and  French  time  is 
9m  218  faster  than  Greenwich  time.  The  system  of  standard  time  is 
so  convenient  that  it  will  eventually  be  extended  to  all  civilized 
countries,  in  all  likelihood. 

Change  of  the  Day  to  an  Observer  travelling  round 
the  Earth. — Suppose  an  observer  to  be  at  Greenwich. 
When  the  mean  Sun  crosses  his  celestial  meridian  it  is 
noon.  Let  us  say  it  is  Monday  noon.  When  the  mean 
Sun  next  crosses  his  celestial  meridian  it  is  Tuesday  noon, 


102  ASTRONOMY. 

and  so  on.  Whenever  the  mean  Sun  crosses  the  meridian 
of  any  observer  anywhere  on  the  Earth  it  is  noon  for  him. 
If  he  is  east  of  Greenwich  the  San  crosses  his  celestial 
meridian  before  it  reaches  the  Greenwich  meridian,  and  his 
time  is  later  than  the  Greenwich  time.  If  he  is  west  of 
Greenwich  the -Sun  does  not  cross  his  celestial  meridian 
until  after  it  has  crossed  that  of  Greenwich,  and  the  Green- 
wich time  is  later. 

Suppose  a  traveller  to  set  out  from  Greenwich  carrying  a  watcli 
with  him  that  shows  not  only  the  Greenwich  hour  and  minute,  but 
also  the  day.  It  would  be  easy  to  have  a  watch  made  with  a  day- 
hand  that  went  forward  one  number  (of  days)  every  time  the  hour- 
hand  marked  another  24  hours  elapsed.  Suppose  this  observer  to 
carry  a  card  also,  on  which  he  makes  a  mark,  thus  |  every  time  Hie 
Sun  crosses  his  celestial  meridian.  He  makes  a  mark  for  every  one 
of  his  noons.  Suppose  him  to  travel  eastwards  round  the  globe. 

When  he  comes  to  Sicily  (15°  =  1  hour  of  longitude  east  of  Green- 
wich) the  local  time  will  be  1  P.M.  of  Monday,  when  his  watch  shows 
noon  of  Monday.  At  Alexandria  in  Egypt  (30°  =  2  hours  of  longi- 
tude east  of  Greenwich)  the  local  time  will  be  2  P.M.  when  his  watch 
shows  noon,  and  the  day  will  be  the  same  as  the  Greenwich  day. 

If  he  goes  to  the  Fiji  Islands  (180°  =  12  hours  of  longitude  east  of 
Greenwich)  he  will  find  the  date  later  there  than  the  date  he  carries 
with  him  in  his  watch.  The  local  time  at  Fiji  will  be  12  hours  later 
than  his.  It  will  be  Monday  midnight  (and  thus  the  beginning  of 
Tuesday)  when  his  watch  marks  Monday  noon.  This  is  natural 
enougn.  He  is  travelling  eastwards  and  the  Sun  crosses  these  east- 
ern meridians  before  it  crosses  that  of  Greenwich.  When  he  reaches 
St.  Louis  (270°  =  18  hours  of  longitude  east  of  Greenwich)  the  date 
there  would  be,  on  the  same  principle,  18  hours  later  than  the  Green- 
wich date.  When  his  watch  marks  Monday  noon  the  people  there 
might  call  the  time  18  hours  later  ;  that  is,  Tuesday  6  A.M.  (12h  (noon) 
•f  18h  -  30h,  and  30h  -  24h  =  6h).  But  in  fact  they  call  the  day  Mon- 
day instead  of  Tuesday,  though  they  call  the  hour  corresponding  to 
Greenwich  noon  6  A.M.  Instead  of  reckoning  their  time  to  be  18 
hours  more  (later)  than  Greenwich  time,  they  reckon  it  to  be  6  hours 
less  (earlier).  The  18  hours  more  that  they  fail  to  count  at  all  and 
the  6  hours  less  make  up  24  hours  =  1  day.  The  traveller  has  thus 
gained  a  day  on  his  journey. 

When   he  finally  arrives   at  Greenwich  again   his  watch  agrees 


GRANGE  OF  THE  DAT.  103 

with  the  Greenwich  reckoning  as  to  hours  and  minutes.  The  day- 
hand  of  the  watch  shows  that  he  has  been  away  for  100  days  (let  us 
say),  but  his  card  shows  101  marks  on  it.  The  Sun  has  somehow 
passed  his  celestial  meridian  once  more  than  the  number  of  days 
elapsed.  To  make  the  name  of  his  day  agree  with  the  name  of  the 
day  used  in  Hawaii,  the  United  States,  and  England  he  has  to  drop 
one  day.  How  is  it  that  he  has  gained  a  whole  day  in  travelling 
eastwards  round  the  Earth? 

When  the  Sun  crosses  the  celestial  meridian  of  an  observer  it  is 
noon  for  him.  If  the  observer  stays  at  one  spot  on  the  Earth  the 
Earth  itself,  in  turning  on  its  axis  eastwardly,  brings  his  celestial 
meridian  to  and  past  the  Sun  daily.  If  the  observer  travels  round 
the  Earth  towards  the  east  to  meet  the  Sun  his  own  travels  will  move 
his  celestial  meridian  eastward  a  little  every  day.  The  Sun  will  pass 
his  meridian  101  times  if  he  has  himself  gone  round  the  Earth  in  100 
days.  One  hundred  of  the  transits  of  the  Sun  will  be  due  to  the 
rotation  of  the  Earth  on  its  axis.  One  of  them  will  be  due  to  his  own 
circumnavigation  of  the  globe. 

If  instead  of  going  eastwards  the  observer  (with  his  watch  and  his 
card)  should  travel  westwards  round  the  globe  he  would  find  the 
local  time  at  Washington  five  hours  less  (earlier)  than  the  Greenwich 
time.  At  St.  Louis  the  local  time  would  be  six  hours  less  (earlier). 
At  San  Francisco  it  would  be  eight  hours  less  (earlier).  When  his 
watch  marks  Greenwich  noon  of  Monday  the  people  of  San  Francisco 
will  call  the  date  4  A.M.  of  Monday— eight  hours  less  (earlier)  than 
Greenwich. 

When  he  reaches  India  or  Germany  he  will  find  his  Monday  is  not 
called  Monday  but  Tuesday.  When  he  returns  to  Greenwich  he  will 
find  that  his  reckoning  agrees  with  the  Greenwich  reckoning  in  every 
respect  but  one.  His  watch  will  show  the  Greenwich  hour  and  minute 
exactly.  His  watch  shows  that  he  has  been  absent  for  100  days,  let 
us  say.  But  his  card  shows  that  he  has  had  only  99  noons.  In  going 
round  the  world  to  the  westward,  away  from  the  Sun,  he  has  lost  one 
whole  day.  If  he  had  remained  in  Greenwich  the  Earth's  rotation 
would  have  brought  his  celestial  meridian  to  the  Sun  and  past  it  100 
times.  But  in  his  journey  westward  he  has  carried  his  celestial 
meridian  with  him  and  moved  it  away  from  the  Sun.  The  Earth  has 
turned  round  100  times  during  his  absence,  but  the  Sun  has  only 
crossed  his  (travelling)  meridian  99  times.  Thus  he  has  lost  a  day 
by  travelling  completely  round  the  Earth  westwards — away  from 
sunrise.  If  he  had  travelled  towards  sunrise — eastwards — he  would 
have  gained  a  day,  as  we  have  just  seen. 


104  ASTRONOMY. 

The  Earth  turns  round  just  100  times  in  a  certain  inter- 
val of  time,  and  there  is  never  any  trouble  in  keeping  the 
account.  Those  persons  who  stay  in  one  place  (as  at 
Greenwich)  have  simply  to  count  the  number  of  transits  of 
the  Sun  over  their  celestial  meridian.  Those  persons  who 
travel  westwards  must  add  a  day  when  they  cross  the 
meridian  of  Fiji  (180°  from  Greenwich).  Those  persons 
who  travel  eastivards  must  subtract  a  day  at  this  meridian, 
which  is  called  the  international  date-line  (meaning  change- 
of-date  line). 

When  Alaska  was  transferred  from  Russia  to  the  United 
States  it  was  found  that  one  day  had  to  be  dropped.  The 
Russian  settlers  had  brought  their  Asiatic  date  with  them, 
while  we  were  using  a  reckoning  less  by  one  day  because 
our  count  was  brought  from  Europe. 

Ships  in  the  Pacific  Ocean  passing  the  meridian  of  180° 
add  a  day  going  westwards  and  subtract  a  day  going  east- 
wards. 

It  is  to  be  noted  that  the  place  where  the  change  of  date  is  made 
depends  upon  civil  convenience  and  not  upon  astronomical  necessity. 
The  traveller  must  necessarily  change  his  date  somewhere  on  his 
journey  round  the  world.  It  is  convenient  for  trade  that  two  adja- 
cent countries  should  have  the  same  day-names;  so  that  the  date-line 
in  actual  use  deflects  slightly  from  the  180th  meridian.  All  Asia  is 
to  the  west  of  this  line ;  all  America,  including  the  Aleutian  Islands, 
is  east  of  it.  Samoa  is  east  of  it,  but  the  Tonga  group  and  Chatham 
Island  are  west  of  it. 

—  Define  a  sidereal  day,  a  so^r  day,  a  mean-solar  day.  Which 
of  the  three  is  the  shorter  ?  Why  is  a  sidereal  day  shorter  than  a 
mean  solar  day  ?  What  is  local  time  ?  What  measures  the  difference 
of  longitude  between  two  places  on  the  Earth  ?  Describe  how  to  de- 
termine the  difference  of  longitude  between  Boston  and  San  Fran- 
cisco by  the  transportation  of  chronometers— by  the  comparison  of 
clocks  by  telegraph.  How  does  a  sailor  determine  his  longitude  from 
Greenwich  at  sea  ?  Give  an  account  of  standard  time  as  employed  in 
the  United  States.  Into  how  many  sections  is  the  country  divided  ? 
Name  the  four  kinds  of  time  employed.  Four  watches  keeping  the 


LATITUDE.  105 

standard  time  of  San  Francisco,  Denver,  St.  Louis,  and  Philadel- 
phia are  laid  side  by  side  : — How  will  their  standard  times  differ? 
How  will  their  minutes  and  seconds  compare  with  Greenwich  time? 
What  time  is  used  by  most  ships?  Change  of  the  Day.  When  is  it 
noon  to  any  observer?  If  the  observer  is  E.  of  Greenwich  does  his 
noon  occur  earlier  or  later  than  the  noon  of  Gieenwich?  Explain 
why  it  is  that  an  observer  travelling  completely  round  the  Earth  to 
the  eastwards — towards  sunrise — gains  a  day  ;  and  why  an  observer 
travelling  completely  round  the  Earth  westwards  away  from  sunrise 
loses  a  day. 

17.  METHODS  OF  DETERMINING  THE  LATITUDE  OF  A 
PLACE  ON  THE  EARTH.  Latitude  from  Circumpolar 
Stars. — In  the  figure  suppose  Z  to  be  the  zenith  of  the 
observer,  HZRN  his  meridian,  P  the  north  pole,  HR  his 
horizon.  Suppose  8  and  S'  to  be  the  two  points  where 
a  circumpolar  star  crosses  the  meridian,  as  it  moves  around 


FIG.  54. 

The  latitude  of  a  place  on  the  earth  can  be  determined  by  measuring 
the  zenith  distances  of  a  circumpolar  star  at  its  two  culminatic 


ions. 


the  pole  in  its  apparent  diurnal  orbit.  PS  =  PS'  in  the 
star's  north-polar-distance,  and  PH  =  0  =  the  latitude 
of  the  observer. 


106  ASTRONOMY. 


Therefore  <P  =  90°  -  {  ZS  \  ZS'  j-  .  ' 

Z$  and  ,£$  '  can  be  measured  by  the  sextant  or  by  the 
meridian-circle,  as  will  be  explained  in  the  next  chapter. 
Granted  that  these  arcs  can  be  measured,  it  is  plain  that 
the  latitude  of  a  place  is  known  as  soon  as  they  are  known. 
Latitude  by  the  Meridian  Altitude  of  the  Sun  or  of  a 
Star.  —  jn  the  figure  Z  is  the  observer's  zenith,  P  the  pole, 

HH  the  horizon,  PZH  the 
observer's  meridian,  Q  a 
point  of  the  celestial  equa- 
tor. The  star  S  is  on  the 
meridian  (and  just  at  its 
greatest  altitude  at  that  in- 
stant). Its  altitude  US  can 
be  measured  by  one  of  the 
instruments  described  in  the 

The  latitude  of  a  place  on  the  earth  next   chapter.       ZS  IS  there- 

(of  a  ship  at  sea)  can  be  determined  .           VrmwTi       for     7K  —  Q0° 

t>y  measuring  the  meridian  altitude  *Ore    KHOWn,     1     P    Ato  - 

of  the  sun  (or  of  a  star).  _  flS        Q$  jg   t]je   declina- 

tion of  the  Sun   (or  of  a   star),  and  QS  is  given  in  the 

Nautical  Almanac. 

ZS  -f  QS  =  QZ  =  the  declination  of  the  observer's  zenith, 


or 


-[-   £   =    0   =  the  latitude  of  the  observer. 

If  the  star  (or  Sun)  S'  culminates  north  of  the  zenith 

' 

QS'  -  ZS'=  QZ, 


or 

d    -     C    =  0. 


This  is  the  method  uniformly  used  at  sea,  where  the 


PARALLAX.  107 

meridian  altitude  of  the  Sun  is  measured  every  day  with 
the  sextant.  The  meridian  altitudes  of  stars  are  often 
measured  at  sea,  by  night,  to  determine  the  latitude. 

—  Explain  how  to  determine  the  latitude  of  a  place  on  the  Earth 
by  measuring  the  zenith  distances  of  a  circumpolar  star  at  its  upper 
and  at  its  lower  culmination.  Draw  a  diagram  to  illustrate  the 
method.  Explain  how  to  determine  the  latitude  of  a  place  on  the 
Earth  by  measuring  the  meridian  altitude  of  the  Sun. 

18.  Parallaxes  of  the  Heavenly  Bodies. — The  apparent 
position  of  a  body  (a  planet,  for  instance)  on  the  celestial 
sphere  remains  the  same  as  long  as  the  observer  is  fixed.  If 
the  observer  changes  his  place  and  the  planet  remains  in 
the  same  position,  the  apparent  position  of  the  planet  will 
change.  The  change  in  the  apparent  position  of  a  planet 
due  to  a  change  in  the  position  of  the  observer  is  called  the 


FIG.  56.— PARALLAX. 

Change  in  the  apparent  position  of  a  star  due  to  a  change  in  the  place  of 
the  observer. 

parallax  of  the  planet.  To  show  how  this  is  let  CH'  be 
the  Earth,  C  being  its  centre.  S'  and  S"  are  the  places 
of  two  observers  on  the  surface.  Z'  and  Z"  are  their 
zeniths  in  the  celestial  sphere  Hl  P".  P  is  a  planet.  (P  is 
drawn  near  to  the  Earth  to  save  space  in  the  figure.  If 
it  were  drawn  at  its  proper  proportional  distance  for  the 


108  ASTRONOMY. 

Moon,  which  is  the  nearest  celestial  body  to  the  Earth 
(240,000  miles  distant),  the  drawing  would  show  P  more 
than  two  feet  distant  from  (7.) 

8'  will  see  P  in  the  apparent  position  P'.  8"  will  see 
P  in  the  apparent  position  P".  That  is,  two  different 
observers  will  see  the  same  object  in  two  different  appar- 
ent positions.  If  the  observer  8 '  moves  along  the  surface 
directly  to  $",  the  apparent  position  of  P  on  the  celestial 
sphere  will  appear  to  move  from  P  '  to  P  ".  This  change 
is  due  to  the  parallax  of  P. 

If  the  observers  S'  and  S"  could  go  to  the  centre  of  the 
Earth  (C)  they  would  both  see  the  planet  P  in  the  posi- 
tion P,. 

Astronomical  observations  made  by  observers  at  points 
on  the  Earth's  surface  (as  at  Greenwich  and  Washington) 
are  corrected,  therefore,  by  calculation,  so  as  to  reduce 
them  to  what  they  would  have  been  had  the  observers  been 
situated  at  the  centre  of  the  Earth,  from  which  point  the 
planet  would  be  seen  always  in  one  position  on  the  celestial 
sphere. 

The  student  can  try  an  experiment  in  the  classroom  that  will  illus- 
strate  what  parallax  is  (See  Fig.  57).  Let  him  set  up  a  pointer  some- 
where in  the  middle  of  the  room  and  look  at  it  from  a  point  near  the 
south-west  corner  of  the  room  I.  The  line  joining  his  eye  and  the 
pointer  will  meet  the  opposite  wall  in  a  point  1.  One  of  his  class- 
mates under  his  direction  should  mark  the  point  1.  Now  let  the 
observer  go  to  another  station,  II.  He  will  see  the  pointer  projected 
against  the  opposite  wall  at  2,  and  this  point  should  be  marked  also. 
If  he  goes  to  III  the  pointer  will  be  seen  projected  at  3,  and  so  on. 
The  change  in  the  apparent  position  of  the  pointer  on  the  opposite 
wall  due  to  the  change  in  the  observer's  place  is  the  parallax  of  the 
pointer.  The  real  position  of  the  pointer  has  not  changed  at  all. 

While  the  observer  has  moved  from  I  to  III  the  apparent  posi- 
tion of  the  pointer  has  moved  from  1  to  3.  Any  one  who  is  making 
a  railway  journey  can  find  many  examples  of  parallactic  changes  of 
apparent  position  by  fixing  his  eye  on  points  in  the  landscape  They 
will  appear  to  move  relatively  to  each  other  as  the  observer  moves. 


PARALLAX. 


109 


In  Fig.  58  suppose  that  C  represents  the  Sun,  around  which  the 
Earth  8'  moves  in  the  nearly  circular  orbit  8'  8"  H'.  S'C  is  no 
longer  4000  miles  as  in  the  last  example,  but  it  is  93,000,000  miles. 
Suppose  P  to  be  a  star.  When  the  Earth  is  in  the  position  8'  the 

1V.E. ,S.E. 


N.W.  - 


1 

1 

III 

t 

2 

0          n 

Pointer 

1 

1 

3 

I 

s.w. 


FIG.  57. 
To  illustrate  the  parallax  of  a  body. 

star  will  be  projected  on  the  celestial  sphere  at  P' ;  when  the  Earth 
has  moved  to  8",  the  star  will  be  projected  on  the  celestial  sphere  at 
P".  While  the  Earth  is  moving  from  S'  to  8"  the  star  P  will  appear 
to  move  from  P'  to  P".  It  will  not  really  move  iu  space  at  all,  but 


FIG.  58. — THE  ANNUAL  PARALLAX  OF  A  STAR. 

its  apparent  position  on  the  celestial  sphere  will  appear  to  move  be- 
cause the  observer  moves.  If  the  observer  were  at  the  Sun  (C)  in- 
stead of  on  the  Earth  (at  8')  he  would  see  the  star  at  P, ;  if  the  ob- 
server 8"  were  a,t  the  Sun  (C)  he,  also,  would  see  the  star  at  P^ 


110  ASTRONOMY. 

Observations  made  at  different  points  of  the  Earth's  orbit  (at  dif- 
ferent times  of  the  year,  that  is)  are  reduced,  by  calculation,  to  what 
they  would  have  been  if  the  observer  had  made  them  from  the  Sun 
instead  of  from  the  Earth. 

One  important  point  should  be  especially  noted  here.  If  the  dis- 
tance of  Pfrom  C,  in  the  last  figure,  increases  the  changes  in  its  posi- 
tions Pf,  P"  due  to  changes  in  the  position  of  the  observer  (/S't  S"  etc.) 
will  be  .less  and  less.  The  student  can  prove  this  by  drawing  the 
figure  three  times,  making  the  small  circle  and  the  points  S',  S"  the 
same  in  each  figure.  In  the  first  drawing  let  him  make  CP  —  1  inch, 
in  the  second  make  CP  —  2  inches,  in  the  third  make  CP  —  3  inches. 
The  greater  the  distance  of  a  body  from  the  observer,  the  less  the 
change  in  the  body's  apparent  position  due  to  a  given  change  in  the 
observer's  place. 

The  Moon  is  240,000  miles  away  from  the  Earth.  An 
observer  at  Greenwich  will  see  the  Moon  projected  on  the 
celestial  sphere  in  a  place  quite  different  from  the  Moon's 
place  as  seen  from  the  Cape  of  Good  Hope.  Jupiter  is 
over  400,000,000  miles  away  from  the  Earth.  Observers 
at  Greenwich  and  at  the  Cape  of  Good  Hope  will  see  it  at 
different  apparent  positions  on  the  celestial  sphere,  but 
these  positions  will  not  be  very  far  apart.  Sirius  is  over 
200,000,000,000,000  miles  away  from  the  Earth.  Observers 
at  Greenwich  and  at  the  Cape  of  Good  Hope  will  see  it  in 
the  same  position.  That  is,  we  have  no  telescopes  that 
will  measure  its  exceedingly  small  change  of  place.  An 
observer  at  Greenwich  looking  at  Sirius  in  January  will 
see  it  in  a  position  on  the  celestial  sphere  only  a  very 
little  different  from  the  place  in  which  the  same  observer 
will  see  it  in  July.  Yet  the  observer  has  travelled  half 
round  the  Earth's  orbit  meanwhile,  and  his  place  in  July 
is  about  186,000,000  miles  distant  from  his  place  in 
January.  (The  distance  from  the  Earth  to  the  Sun  is 
about  93,000,000,  and  twice  that  is  186,000,000.)  It  is 
clear  that  if  we  can  measure  the  amount  of  displacement 
of  the  Moon,  of  Jupiter,  of  Sirius,  due  to  a  known  change 
in  the  observer's  place,  there  must  be  a  way  to  calculate 


PAKALLAX.  Ill 

how  far  off  these  bodies  are  to  suffer  the  observed  changes 
in  their  apparent  positions. 

—  What  is  the  parallax  of  a  star  (or  of  the  Sun,  or  of  a  planet)? 
To  what  point  of  the  Earth  are  observations  made  on  its  surface  re- 
duced? Why  are  they  so  reduced?  Describe  a  simple  experiment 
to  illustrate  parallactic  changes.  Is  there  a  change  in  the  apparent 
position  of  stars  due  to  the  revolution  of  the  Earth  round  its  orbit  ? 
Draw  a  figure  to  illustrate  this.  To  what  point  within  the  Earth's 
orbit  are  observations  reduced  to  avoid  such  parallactic  changes? 
Prove  by  three  drawings  that  the  further  a  star  is  from  the  observer 
the  less  are  its  parallactic  changes  due  to  a  given  change  in  the 
observer's  place. 


CHAPTER   VII. 
ASTRONOMICAL   INSTRUMENTS. 

19.  Astronomical  Instruments  —  Telescopes. — Celestial 
Photography — The  Nautical  Almanac. — The  instruments 
of  astronomy  are  telescopes  that  enable  us  to  see  faint 
stars  which  otherwise  we  should  not  see  at  all ;  or  telescopes 
and  circles  combined,  that  enable  us  to  measure  angles; 
or  timepieces  (chronometers  and  clocks)  that  enable  us  to 
measure  intervals  of  time  with  exactness;  spectroscopes, 
that  enable  us  to  analyze  the  light  from  a  heavenly  body 
and  to  say  what  chemical  substances  it  is  made  of,  etc. 
All  these  instruments  have  been  gradually  perfected  until 
most  of  them  are  now  extremely  accurate,  but  many  of 
them  had  very  humble  beginnings. 

Clocks. — The  first  timepieces  were  sun-dials,*  water- 
clocks,  etc.  The  ancients  noticed  that  the  shadow  of  an 
obelisk  moved  during  the  day.  When  the  Sun  was  rising 
in  the  east  the  shadow  of  an  obelisk  lay  opposite  to  the 
Sun  towards  the  west.  As  the  Sun  rose  higher  in  the  sky 
and  moved  towards  the  meridian  the  shadow  moved  towards 
the  north  and  grew  shorter.  When  the  Sun  was  exactly 
south  of  the  obelisk  (on  the  meridian  due  south  of  the  ob- 
server and  at  its  greatest  altitude)  the  shadow  lay  exactly 
to  the  north  and  it  was  the  shortest.  As  the  Sun  drew 
towards  the  west  the  shadow  moved  towards  the  east  and 

*  We  know  that  a  Sun-dial  was  set  up  in  Rome  B.C.  263.  PLAU- 
TUS  speaks  of  a  slave  who  complained  of  Sun-dials  and  the  new- 
fangled hours.  In  old  time,  he  says,  he  used  to  eat  when  he  was 
hungry  ;  now  the  time  when  he  gets  his  rnea.ls  depends  on  the  Sun  ! 


FIG.  59. — GALILEO. 
Born  1564;  died  1642. 


113 


114  ASTRONOMY. 

grew  longer;   and  as  the  Sun  was  setting  in  the  west  the 
shadow  pointed  towards  the  east.     A  circle  was  traced  on 

the  ground  round  the  obelisk 
and  the  north  point  of  the  circle 
was  marked.  When  the  shadow 
fell  at  this  point  the  San  was 
due  south  at  noon  and  the  day 
was  half  over.  This  was  the 
first  timepiece.  By  dividing 
the  circle  into  smaller  parts  the 
day  was  likewise  divided  into 
parts.  Some  of  the  churches 
in  Italy  have  sun-dials  laid  out 
on  their  floors  so  that  a  spot  of 
sunlight  admitted  through  the 
south  wall  traverses  an  arc 
divided  into  hours  and  minutes. 
The  student  should  set  up  a  verti- 
cal pole  and  trace  a  circle  around  it 
and  divide  the  circle  into  parts,  using 
his  watch  to  get  the  hour  marks.  The 
circular  dial  of  Fig.  60  is  horizontal 
FIG.  60.— A  SUN  DIAL.  and  XII  is  towards  the  north. 

It  was  not  easy,  in  ancient  times,  to  mark  the  places  on 
the  dial  that  corresponded  to  the  hours  and  to  the  smaller 
divisions  of  time.  These  were  often  counted  by  water- 
clocks  or  sand-clocks,  in  which  water  or  sand  poured  from 
a  box  through  a  hole  in  the  bottom.  The  lowering  of  the 
upper  surface  of  the  water  or  sand  marked  the  passage  of 
time.  The  common  hour-glass  is  a  sand-clock.  Candles 
were  marked  by  lines  at  equal  intervals  and  equal  intervals 
of  time  were  counted  by  the  burning  of  equal  lengths  of 
wax.  The  student  can  construct  timepieces  in  this  way 
and  he  can  test  their  accuracy  by  a  watch  or  clock. 

GALILEO  noticed  about  the  year  1600  that  a  given 
pendulum  always  made  its  swings  in  equal  times  no  matter 


ASTRONOMICAL  INSTRUMENTS.  115 

whether  it  swung  through  large  arcs  or  small  ones.  A 
long  pendulum  swung  slowly;  a  short  pendulum  swung 
faster;  but  each  pendulum  had  its  own  time  of  swinging 
and  it  always  swung  in  that  time.  A  pendulum  about 
inches  long  made  a  swing  in  one 
second  (from  its  lowest  point  to  its  ^^7-^ 

lowest  point  again  in  one  second). 


It  made  86,400  vibrations  in  a 
mean  solar  day.*  Intervals  of  time 
could  now  be  accurately  divided. 


The  student  should  make  a  pendulum 
for  himself.  A  very  good  method  is 
described  in  Allen's  Laboratory  Physics 
as  follows : 

Near  !S,  which  may  be  the  edge  of  a 
table  or  shelf,  is  screwed  a  spool  S'. 
The  screw  is  "set  up"  until  the  spool 
turns  with  considerable  friction.  A 
string  is  wound  around  the  spool  and  is 
held  in  place  by  passing  through  the  slot 
of  another  screw,  R,  inserted  horizontally 
in  the  edge  of  the  support.  The  lower 
end  of  the  string  passes  through  a  hole 
in  a  ball  B,  which  forms  the  pendulum-  {&) 

boh.     The  length  of  the  pendulum  may  jp 

be  varied  by  turning  the  spool  so  as  to  FIG.  61. — A  HOME-MADE 
wind  or  unwind  the  string.  Small  PENDULUM  WHOSE 
adjustments  are  best  made  by  gently  LENGTH  CAN  BE 
turning  the  spool.  READILY  VARIED. 

Many  improvements  have  been  made  in  pendulum-clocks 
since  they  were  first  invented  by  HUYGHENS  (pronounced 
hi'genz)  in  1657,  and  they  are  now  extraordinarily  accu- 
rate. Chronometers  are  merely  very  perfect  watches. 
Their  motive  force  is  a  coiled  spring,  and  they  can  be 
transported  by  sea  or  land  while  they  are  running,  which 
is  not  true  of  clocks,  of  course. 

*  00  X  60  X  24  =  86,400, 


116  ASTRONOMY. 

Circles. — Angles  can  be  measured  by  circles  divided  to 
degrees,  etc.  If  the  arc  S'S*  is  so  divided  and  if  it  has  a 
radial  bar  ES'  that  can  be  moved  around  a  pin  at  the 
centre  of  the  circle  at  E,  the  angle  between  any  two  stars 
can  be  measured  in  the  following  way : 

1st.  Place  the  circle  so  that  its 
plane  passes  through  the  two  stars 
S'  and  $2  when  the  eye  is  at  E. 

2d.  Point  the  bar  at  S'  and 
read  the  divisions  on  the  circle — 
as  10°  5',  for  example.  The  eye 
will  still  be  at  E,  of  course. 

3d.  Point  the  bar  at  S*  and  read 

FIG.   62. -MEASUREMENT  the  circle"as  22°  n/- 
OP  ANGLES  BY  A  CIRCLE      The  angle  between  the  two  stars 
(OR   BY   A    PART   OF   A  s,m*  ig  12o  g,    the  difference  of 

v/IRCLEJ. 

the  two   readings.     In  the  figure 

the  angle  S'ES*  is  about  12°;  S*ES*  isabout  22°;  S*£S3 
is  about  30°;  S'ES4  is  about  64°. 

Before  the  telescope  was  invented  the  bar  ES'  was  pro- 
vided with  sights  like  the  sights  on  a  rifle.  One  sight  was 
at  E  (the  place  of  the  eye),  the  other  at  the  further  end  of 
the  bar.  The  unavoidable  error  of  directing  such  a  bar  to 
a  star  is  about  1'  of  arc,  so  that  the  positions  of  stars  before 
the  telescope  was  invented  were  liable  to  errors  of  1'  or  so. 
The  eye  cannot  detect  a  change  of  direction  less  than  about 
one  minute  of  arc.  The  bar  and  its  sights  are  nowadays 
replaced  by  a  telescope,  and  the  positions  of  stars  deter- 
mined by  such  a  combination  of  a  circle  and  a  telescope  are 
affected  by  errors  of  less  than  1".  The  precision  is  more 
than  60  times  greater. 

The  student  will  do  well  to  make  a  half-circle  in  the  following 
way:  Cut  a  half-circle  8£  inches  in  diameter  out  of  a  piece  of  thick 
hard  pasteboard,  leaving  a  knob  or  projection  about  1  inch  square  at 
(7.  Through  this  knob  bore  a  hole  with  an  awl  at  the  exact  centre  of 


ASTRONOMICAL  INSTRUMENTS.  117 

the  circle.     Order  from  Keuffel  &  Esser,  opticians,  No.  127  Fulton 
street,  New  York  city,  a  paper  circle,  8  inches  in  diameter,  divided 
to  30'.     It  is  No.  1296  of  their  cata- 
logue.    It   can  be  sent  by  mail  and 
will   cost  20  cents.     Cut  the  paper- 
circle  in  two  along  a  diameter  and 
fasten  it  to  the  pasteboard,  making 
the  centre  of  the  paper-circle  coin- 
cide with  the  centre  of  the   paste- 
board  circle.      Make   a  narrow  flat 
light  wooden  arm  for  the  index-arm,      FIG.  63. — A  HALF  CIRCLE. 
like  Fig.  64  :  A  is  the  centre  of  the 

circle.  The  arm  must  revolve  about  a  pin  (or  a  rivet)  at  A.  B  and 
C  are  the  sights.  Two  common  pins  will  do.  D  is  an  index  mark,  or 
pointer,  drawn  on  the  arm.  All  angles  are  read  from  this  mark,  a, 
b,  c,  d,  are  four  divisions  of  the  paper  circle.  If  a  =  17°,  b  =  18°, 
c  =  19°,  d  =  20°,  then  the  reading  of  the  pointer  is  18±  degrees.  In 
using  the  circle  the  eye  must  be  at  A  ;  the  observer  looks  along  the 


A     B 


FIG.  64.— INDEX  ARM  FOR  A  DIVIDED  CIRCLE. 


sights  EC  and  moves  the  arm  till  the  sights  and  the  star  are  in  the 
same  line.  To  measure  the  angle  between  two  stars  the  plane  of  the 
circle  must  be  put  in  the  plane  of  the  eye  and  of  the  two  stars  and 
kept  there.  To  measure  the  altitude  of  the  celestial  pole  (the  latitude 
of  the  observer)  the  plane  of  the  circle  must  be  vertical.  Two  read- 
ings'must  be  made:  1st,  when  the  index  arm  is  horizontal  (a  level 
will  show  this)  and  2d,  when  the  arm  points  to  Polaris.  A  light 
plumb  line  suspended  from  the  centre  of  the  circle  will  mark  the 
vertical  direction,  so  that  zenith  distances  can  be  measured. 

Invention  of  the  Telescope. — The  first  telescope  used  in 
astronomy  was  invented  by  GALILEO  in  1609.*  It  was  like 
a  long  single-barreled  opera-glass.  The  best  of  GALILEO'S 
telescopes  magnified  only  about  30  times;  but  this  was 

*  Eleven  years  before  the  Pilgrims  landed  at  Plymouth.  Prob- 
ably no  one  of  them  had  even  heard  of  this  invention. 


118  ASTRONOMY. 

enough  to  explain  many  things  that  had  heen  mysteries 
for  two  thousand  years.  The  Moon's  face  was  very  well 
shown  in  GALILEO'S  instruments  and  the  mountains  of  the 
Moon  were  then  discovered.  The  Milky  Way  was  shown 
to  consist  of  closely  crowded  stars.  If  the  student  will 
look  at  the  Moon's  face  and  at  the  Milky  Way  with  a  com- 
mon opera-glass  (which  magnifies  about  3  times)  he  will 
see  far  more  than  with  the  eye.  The  true  shapes  of  the 
planets  Venus  and  Mercury  were  made  out  for  the  first 
time.  It  was  seen  that  they  had  phases  like  the  Moon 
(they  were  sometimes  crescent,  sometimes  full,  etc.),  and 
this  discovery,  more  than  any  other,  helped  to  overthrow 
the  theory  of  PTOLEMY  that  the  Earth  was  the  centre  of 
the  universe,  and  to  establish  the  theory  of  COPERNICUS, 
that  the  centre  of  our  system  was  the  Sun,  not  the  Earth. 
GALILEO  discovered  four  satellites  of  Jupiter  also  and 
showed,  in  this  way,  that  "  the  seven  planets"  (Sun, 
Moon,  Mercury,  Venus,  Mars,  Jupiter,  Saturn)  were 
seven  in  number,  not  because  of  some  mystic  law,  but 
simply  because  the  other  bodies  of  the  system  happened 
to  be  too  faint  to  be  seen  with  the  unassisted  eye. 

^  Seven  had  been  a  mystical  number  since 

the  times   of  PYTHAGORAS.     There  were 
seven  planets,  seven   days  of  the   week, 
seven  wise  men  of  Greece,  seven  cardinal 
virtues,  seven  deadly  sins,  seven  notes  of 
music  in  the  octave,  etc.     Men  regarded 
this  number  as  if  it  were  sacred  in  itself; 
and  they  were  not  willing  to  believe  their 
own  eyes  when  more  than  seven  heavenly 
JBLE  -  CONVEXU"  bodies  were  shown  to  them.     The  greatest 
LENS  OP  GLASS,  value  of  GALILEO'S  discovery  was  precisely 
its  demonstration  that  men  must  accept  a  scientific  fact 
when   it   is  proved.;    and  that  Nature  was  governed  by 
laws  of  a  different  kind  from  the  fanciful  analogies  of  the 


ASTRONOMICAL  INSTRUMENTS.  119 

imagination.  From  the  time  of  GALILEO  men  began  to 
think  about  Nature  in  a  new  way  and  the  discoveries  of  his 
telescope  are,  for  that  reason,  the  most  important  scientific 
discoveries  ever  made. 

Construction  of  the  Telescope. — Long  before  the  time  of 
GALILEO  glass  lenses  had  been  used  for  spectacles.  The 
Emperor  Nero  (died  A.D.  68)  is  said  to  have  employed 
such  a  lens.  It  was  found  that  a  double-convex  lens  made 
out  of  glass  not  only  collected  light,  but  that  if  it  was  held 
in  a  proper  position  it  magnified  the  object  looked  at. 
The  ordinary  hand  reading-glass  is  a  familiar  example  of 
this  fact. 

Figure  66   shows   the  way  in  which  the    reading-glass 


FIG.  66. 

The  reading-glass  C  magnifies  an  object  AB  to  the  size  ab. 

magnifies.  AMB  is  an  object  viewed  by  a  reading-glass 
C.  From  every  point  of  the  object  AB  rays  of  light  issue, 
and  they  go  in  every  direction.  (The  proof  of  this  fact  is 
that  no  matter  where  you  stand  you  can  still  see  AB\  and 
if  you  see  it  there  must  be  rays  that  come  from  AB  and 
reach  your  eye.)  The  bundle  of  rays  that  comes  from  the 
point  A  and  falls  on  the  reading-glass  C  is  c Ad.  No  other 
rays  from  A  fall  on  the  glass.  These  pass  through  the 
glass  and  come  to  a  focus  at  a;  a  is  the  image  of  the  point 
A  of  the  object.  The  point  B  of  the  object  is  sending  out 
rays  in  every  direction.  Some  of  them  fall  on  the  glass — 


120  ASTRONOMY. 

namely  the  bundle  cBd.  This  bundle  of  rays  passes 
through  the  glass  and  comes  to  a  focus  at  Z>;  b  is  the 
image  of  the  point  B  of  the  object.  The  point  M  of  the 
object  is  giving  out  rays  in  every  direction.  Only  those 
that  fall  on  the  glass  can  pass  through  it — namely  the 
bundle  of  rays  cMd.  This  bundle  of  rays  passes  through 
the  glass  and  comes  to  a  focus  at  N.  N  is  the  image  of 
the  point  M  of  the  object.  Every  point  of  the  object  sends 
out  rays,  and  bundles  of  rays  from  every  such  point  pass 
through  the  glass  and  each  such  bundle  comes  to  a  focus 
somewhere  on  the  line  ab  and  forms  an  image  of  the  cor- 
responding point  of  the  object.  All  these  separate  images, 
taken  together,  make  onet  image,  a  picture,  of  the  object. 
ab  is  the  image,  the  picture,  of  AB. 

Now  suppose  that  with  a  second  hand-glass  you  should 
look  at  the  image  ab  just  as  you  looked  at  the  object  AB 
with  the  first  hand-glass.  If  the  second  glass  is  held  in  a 
proper  position  you  can  magnify  the  image  ab  just  as  the 
object  AB  was  originally  magnified.  A  combination  of 
the  two  or  more  lenses  to  make  a  magnified  image  is  a  tele- 
scope. GALILEO'S  invention  was  the  use  of  two  lenses  in 
combination. 

All  refracting  telescopes  (telescopes  in  which  rays  of  light 
from  the  object  are  bent — refracted — by  the  telescope  so  as 
to  form  an  image)  consist  essentially  of  two  lenses.  The 
first  lens  (that  one  nearest  the  star)  is  made  as  large  as  pos- 
sible so  as  to  collect  as  much  light  as  possible.  All  the 
bundles  of  rays  that  fall  upon  it  are  bent — refracted — by 
this  lens  and  brought  to  a  focus;  and  together  they  make 
an  image — a  picture — of  the  object.  This  first  lens  is 
called  the  object-lens  (or  the  object-glass).  Its  sole  use  is 
to  collect  as  many  rays  from  the  object  as  possible  and  to 
form  them  into  an  image — a  picture — at  the  focus.  If 
you  should  hold  a  piece  of  ground-glass  at  the  focus  of  a 
telescope  you  would  see  a  small  picture  on  the  glass — a  pic- 


ASTRONOMICAL  INSTRUMENTS.  121 

tare  of  the  Sun,  of  the  Moon,  of  a  star,  according  as  the 
telescope  was  pointed  to  the  Sun,  the  Moon,  or  a  star.  If 
you  should  put  a  photographic  plate  at  the  focus  you  could 
make  a  photographic  negative  of  the  Sun,  the  Moon,  a 
star. 

The  second  lens  (it  is  called  the  eyepiece)  is  used  to 
magnify  the  image  formed  by  the  object-lens.  Every  tele- 
scope is  provided  with  several  eyepieces.  Some  of  these 
magnify  more  than  others.  If  a  powerful  eyepiece  is  used 
the  telescope  may  magnify  1000  times.  If  one  of  the  less 
powerful  is  employed  it  may  magbify  100  times.  You  can 
change  the  magnifying  power  of  a  telescope  by  changing 
the  eyepiece,  therefore;  and  there  is  not  much  point  to  the 
common  question:  "  How  much  does  this  telescope  mag- 
nify?" The  answer  is  "it  depends  upon  what  eyepiece 
you  are  using."  The  tube  of  a  telescope  is  chiefly  for  the 
purpose  of  keeping  the  object-glass  and  the  eyepiece  at  the 
right  distance  apart. 

It  is  found  that  single  lenses  of  glass  give  imperfect  im- 
ages of  objects.  The  images  from  single  lenses  are  some- 
what distorted  and  they  are  bordered  with  fringes  of  color. 
A  few  experiments  with  a  common  reading-glass  will  prove 
this.  Much  of  the  imperfection 
can  be  avoided  by  making  the 
object-glasses  of  telescopes  out 
of  two  lenses  of  different  kinds 
of  glass  close  together,  as  in 
Fig.  67.  The  light  from  the 
star  first  falls  on  a  lens  of  crown-  FIG.  67.— THE  ACHROMATIC 
glass  and  after  passing  through  OBJECT-GLASS. 

it  falls  on  a  lens  of  flint-glass.  The  two  lenses  act  like  a 
common  convex  lens  in  bringing  the  rays  to  a  focus  to  form 
an  achromatic  or  colorless  image.  The  image  from  such 
an  object-glass  is  much  more  perfect  than  that  formed  by 
a  single  lens.  Eyepieces,  also,  are  made  of  two  or  more 


122 


ASTRONOMY. 


The  telescopes  now  in  use  are  practically  as  per- 
fect as  they  can  be  made  from  the  glass  we  now  have. 

Light-gathering  Power  of  a  Telescope. — It  is  not  merely 
by  magnifying  that  the  telescope  assists  vision,  bat  also  by 
increasing  the  quantity  of  light  received  from  any  object — 
from  a  star,  for  example.  When  the  unaided  eye  looks  at 
any  object,  the  retina  can  only  receive  so  many  rays  as 
fall  upon  the  pupil  of  the  eye.  The  eye  is  itself  a  little 
telescopic  lens  whose  image  is  received  on  the  sensitive  ret- 
ina. By  the  use  of  the  telescope  it  is  evident  that  as  many 
rays  can  be  brought  to  the  retina  as  fall  on  the  entire  ob- 
ject-glass. The  pupil  of  the  human  eye  has  a  diameter  of 
about  one  fifth  of  an  inch,  and  by  the  use  of  the  telescope 
it  is  virtually  increased  in  surface  in  the  ratio  of  the  square 
of  the  diameter  of  the  objective  to  the  square  of  one  fifth 
of  an  inch;  that  is,  in  the  ratio  of  the  surface  of  the  ob- 
jective to  the  surface  of  the  pupil  of  the  eye.  Thus,  with 
a  two-inch  aperture  to  our  telescope,  the  number  of  rays 
collected  is  one  hundred  times  as  great  as  the  number  col- 
lected with  the  naked  eye,  because 

(.2)'  :  (2)'  =  .04  :  4.0 
=    1    :  100. 


With  a  5-inch  object  glass  the  ratio  is 
10     «« 
15     " 
20     " 


625  to  1 

2,500  to  1 

5,625  to  1 

10,000  to  1 

16,900  to  1 

32,400  to  1 


When  a  minute  object,  like  a  small  star,  is  viewed,  it  is 
necessary  that  a  certain  number  of  rays  should  fall  on  the 
retina  in  order  that  the  star  may  be  visible  at  all.  It  is 
therefore  plain  that  the  use  of  the  telescope  enables  an  ob- 
server to  see  much  fainter  stars  than  he  could  detect  with 
the  naked  eye,  and  also  to  see  faint  objects  much  better 


ASTRONOMICAL  INSTRUMENTS.  123 

than  by  unaided  vision  alone.  Thus,  with  a  36-inch  tele- 
scope we  may  see  stars  so  minute  that  it  would  require  the 
collective  light  of  many  thousands  to  be  visible  to  the  un- 
aided eye. 

Eeflecting  Telescopes.— One  of  the  essential  parts  of  a  refracting 
telescope  is  tlie  object-glass,  which  brings  all  the  incident  rays  from 
an  object  to  one  focus,  forming  there  an  image  of  that  object.  In 
reflecting  telescopes  (reflectors)  the  objective  is  a  mirror  of  speculum 
metal  or  silvered  glass  ground  to  the  shape  of  a  paraboloid.  Fig. 
G3  shows  the  action  of  such  a  mirror  on  a  bundle  of  parallel  rays, 


PIG.  68.— THEORY  OP  THE  REFLECTING  TELESCOPE. 

which,  after  impinging  on  it,  are  brought  by  reflection  to  one  focus 
F.  The  image  formed  at  this  focus  can  be  viewed  with  an  eyepiece, 
as  in  the  case  of  the  refracting  telescope. 

The  eyepieces  used  with  such  a  mirror  are  of  the  kind  already  de- 
scribed. In  the  figure  the  eyepiece  would  have  to  be  placed  to  the 
right  of  the  point  F,  and  the  observer's  head  would  thus  interfere 
with  the  incident  light.  Various  devices  have  been  proposed  to  rem- 
edy this  inconvenience,  of  which  the  most  simple  is  to  interpose  a 
small  plane  mirror,  which  is  inclined  45°  to  the  line  AC,  just  to  the 
left  of  F.  This  mirror  will  reflect  the  rays  which  are  moving  towards 
the  focus  .F  (downwards  on  the  page)  to  another  focus  outside  of  the 
main  beam  of  rays.  At  this  second  focus  the  eyepiece  is  placed  and 
the  observer  looks  into  it  in  a  direction  perpendicular  to  A  G  (up- 
wards on  the  page).  See  Fig.  69. 

—  Name  some  of  the  instruments  used  in  astronomy.  Sun-dial. 
Describe  the  motion  of  the  shadow  of  an  obelisk  from  sunrise  to  noon, 
from  noon  to  sunset.  At  what  time  in  the  day  is  the  shadow  of  the 
obelisk  the  shortest  ?  Prove  it  by  a  drawing.  At  what  instant  of 


124:  ASTRONOMY. 

the  day  does  its  shadow  point  due  north?  Say  how  you  could  make 
a  sun-dial  with  a  pole  and  a  common  watch.  Water-clocks.  Tell 
what  they  were.  Pendulums.  How  can  you  make  a  pendulum  that 
swings  in  a  second  of  time?  Divided  circles.  Say  how  you  could  make 
one.  Describe  how  to  use  it  in  measuring  the  angle  between  two  stars 
(the  vertex  of  the  angle  is  at  the  eye).  Telescopes.  When  did  GALILEO 
construct  his  first  telescope?  Draw  a  diagram  to  show  how  a  com- 
mon reading-glass  forms  an  image  of  an  object  at  a  focus.  Define  a 


FIG.  69. 

This  figure  shows  the  way  in  which  the  rays  of  light  move  in  a  reflecting 
telescope.  They  come  from  a  star  as  a  beam  of  light  and  cover  the  whole 
of  the  curved  mirror  at  the  bottom  of  the  tube  (A).  This  mirror  reflects 
them  towards  a  focus  (like  F  in  the  preceding  figure).  Before  the  rays 
reach  the  focus,  they  fall  on  a  small  flat  mirror  which  turns  them  at  right 
angles  to  their  former  direction  and  they  come  to  a  new  focus  (G)  outside 
of  the  telescope-tube.  Here  the  eyepiece  is  placed. 

telescope.  Exactly  what  was  Galileo's  invention?  What  is  a  re- 
fracting telescope  ?  What  is  an  object-glass  ?  an  eye-piece  ?  What  is 
the  sole  purpose  of  the  object-glass?  Why  then  is  it  an  advantage 
to  make  it  as  large  as  may  be  ?  What  is  the  sole  purpose  of  the  eye- 
piece? What  is  the  answer  to  the  question  "How  much  does  this 
telescope  magnify?"  Draw  a  diagram  of  a  reflecting -telescope. 

20.  The  Transit  Instrument. — The  Transit  Instrument 
is  used  to  observe  the  transits  of  stars  over  the  celestial 
meridian.  The  times  of  these  transits  are  noted  by  the 
sidereal  clock,  which  is  an  indispensable  adjunct  of  the 
transit  instrument.  It  stands  near  it  so  that  the  dial  of 
the  clock  can  be  seen  and  so  that  the  beats  of  the  pendu- 
lum can  be  heard  every  second.  A  skilled  observer  can 
estimate  the  time  to  the  nearest  tenth  of  a  second.  The 
first  transit-instrument  was  invented  in  the  XVII  century. 

The  transit  instrument  consists  essentially  of  a  telescope  TT  fast- 
ened to  an  axis  FFat  right  angles  to  it.  The  ends  of  this  axis  ter- 


ASTRONOMICAL  INSTRUMENTS.  125 


FIG.  70.— A  TRANSIT-INSTRUMENT. 


126  ASTRONOMY. 

miuate  in  accurately  cylindrical  pivots  which  rest  in  metallic  bearings 
FF  which  are  shaped  like  the  letter  Y,  and  hence  called  the  Ys. 
The  object-glass  of  the  telescope  is  at  the  upper  end  of  the  tube  in 
the  drawing.  The  eyepiece  is  at  E.  The  telescope  can  be  moved 
so  as  to  point  to  any  point  in  the  celestial  meridian— to  the  zenith, 
the  south  point  of  the  horizon,  the  nadir,  the  north  point,  the  celes- 
tial pole. 

The  Ys  are  fastened  to  two  pillars  of  stone,  brick,  or  iron.  Two 
counterpoises  IF  Ware  connected  with  the  axis  as  in  the  plate,  so  as 
to  take  a  large  portion  of  the  weight  of  the  axis  and  telescope  from 
the  Ys,  and  thus  to  diminish  the  friction  upon  them  and  to  render 
the  rotation  about  FF  more  easy  and  regular.  The  line  FF  is 
placed  accurately  level  ;  and  also  perpendicular  to  the  meridian,  or  in 
the  east  and  west  line.  The  plate  gives  the  form  of  transit  used  in 
permanent  observatories,  and  shows  the  observing  chair  C,  the  re- 
versing carriage  It,  and  the  level  L.  The  arms  of  the  latter  have 
Ys,  which  can  be  placed  over  the  pivots  FF. 

The  reticle  is  a  network  of  fine  spider-lines  placed  in  the  focus  of 
the  objective. 

In  Fig.  71  the  circle  represents  the  field  of  view  of  a  transit  as  seen 
through  the  eyepiece.     The  seven  vertical  lines,  I,  II,  III,  IV,  V, 
VI,  VII,  are  seven  fine  spider-lines  tightly 
stretched  across  a  hole  in  a  metal  plate, 
and  so  adjusted  as  to  be  perpendicular  to 
the  direction  of  a  star's  apparent  diurnal 
motion.    The  horizontal  wires,  guide-wires, 
a  and  6,  mark  the  centre  of  the  field.     A 
star  will   move   across  the   field  of  view 
parallel  to  the  lines  ab  and  will  cross  the 
lines  I  to  VII  in  succession.     The  field  of 
view  is  illuminated  at   night  by  a  lamp 
FIG.  71.— SPIDER-LINES  which  causes  the  field  to  appear  bright. 
IN    THE    Focus    OF  A   Tj)e  wjres  are  ^ark  against  a  bright  ground. 
The  line  of  sight  is  a  line  joining  the  centre 

of  the  object-glass  and  the  central  one,  IV,  of  the  seven  vertical 
wires. 

The  axis  FFis  horizontal;  it  lies  east  and  west.  When 
TT  is  rotated  about  FFthe  line  of  sight  marks  out  the 
celestial  meridian  of  the  place  on  the  sphere. 

How  the  Transit-instrument  is  Used  in  Observation. — It  is  pointed 
at  the  place  where  a  star  is  about  to  CTOSS  the  meridian  in  its  course 


ASTRONOMICAL  INSTRUMENTS.  127 

from  rising  to  setting.  As  soon  as  the  star  enters  the  field  the 
telescope  is  slightly  moved  so  that  the  star  will  cross  between  the 
lines  a  and  &.  As  the  star  crosses  each  spider-line,  I  to  VII,  the 
exact  time  of  its  transit  over  each  line  is  noted.  The  average  of 
these  seven  times  gives  the  time  the  star  crossed  the  middle  line  IV. 
(Seven  observations  are  better  than  one,  and  this  is  why  seven  lines 
are  used.)  Let  us  call  this  time  T.  It  will  be  a  number  giving 
hours,  minutes,  seconds  and  fractions  of  seconds,  as  10h  25m 
37s.  22  for  example.  T  is  then  the  time  by  the  sidereal  clock  when  the 
star  was  on  the  meridian.  When  a  star  is  on  the  celestial  meridian 
of  a  place  the  sidereal  time  is  equal  to  the  right-ascension  of  the  star. 
(See  page  88.)  Suppose  the  right-ascension  of  the  star  that  we 
have  observed  to  be  known  and  to  be  R.  A.  =  10h  25m  36s.  18. 
This  number  is  the  sidereal  time  at  the  instant  of  the  transit  of  the 
star.  But  the  clock  time  was  10h  25m  37'.  22.  Hence  the  clock  is 
too  fast  by  1s.  04. 

By  observing  the  time  (T)  when  a  star  of  known  right- 
ascension  (R.A.)  crosses  the  meridian  we  can  determine 
the  correction  of  the  clock.  The  clock  should  mark  a  si- 
dereal time  equal  to  R.A.  It  does  mark  a  time  T.  Hence 
its  correction  is  R.A.  —  T,  because, 

T-}-  (R.A.  —  T)  —  R.A.  =  the  sidereal  time. 

In  this  way  we  can  set  and  regulate  the  sidereal  clock,  so 
that  its  dial  marks  the  exact  sidereal  time  at  any  and  every 
instant.  (In  practice  we  do  not  move  the  hands  but  allow 
for  its  errors.)  Table  V,  at  the  end  of  the  book,  gives  a 
list  of  the  R.A.  of  a  number  of  stars. 

Now  suppose  the  sidereal  clock  to  be  correct  and  the 
times  of  transit  T\  T*,  T*,  etc.,  of  stars  of  unknown  right- 
ascension  to  be  recorded. 

Then  T1  =  the  R.A.  of  the  first  star, 
T*  =   «      «      «    «  second  star, 
T'  -   "      "      "    "  third  star,  and  so  on. 

The  right-ascension  of  any  and  every  unknown  star  can 
be  Determined  as  soon  as  we  have  the  clock  correction.  It 


128 


ASTRONOMY. 


FIG.  72. — A  SMALL  TRANSIT-INSTRUMENT. 
The  length  of  the  telescope  of  this  instrument  is  about  two  feet. 


ASTRONOMICAL  INSTRUMENTS.  129 

is  in  this  way  that  the  transit  instrument  is  employed  to 
determine  the  right  ascensions  of  unknown  stars. 


FIG.  73.— A  MERIDIAN-CIRCLE. 

The  Meridian-circle. — The  meridian-circle  (or  transit- 
circle)  is  a  combination  of  the  transit-instrument  with  a 


130  ASTRONOMY. 

circle  (or  two  circles)  fastened  to  its  axis.  With  the 
transit-instrument  we  can  determine  the  right-ascensions 
of  stars;  with  the  circle  we  can  measure  their  declinations. 

The  picture  shows  a  meridian-circle.  Its  telescope  is 
pointed  downwards  and  the  eyepiece  is  at  its  upper  end. 
The  instrument  differs  from  the  transit  in  having  two 
finely  divided  circles.  Each  of  these  circles  is  read  by  four 
long  horizontal  microscopes.  The  axis  of  the  instrument 
is  made  level  by  a  hanging-level  which  is  shown  in  the  cut. 
The  level  is,  of  course,  removed  when  observations  of  stars 
are  made.  Meridian-circles  were  first  made  in  the  XIX 
century. 

Such  an  instrument  can  be  used  as  a  transit-instrument 
precisely  as  has  been  described.  Its  circle  can  be  used  to 
determine  the  declinations  of  stars. 

The  telescope  is  moved  (so  as  to  trace  out  the  meridian) 
by  turning  the  horizontal  axis  (  FF,  NN,  in  Fig.  70).  As 
the  axis  turns  the  circles  turn  with  it.  The  angle  through 
which  they  turn  can  be  determined  by  noticing  how  many 
degrees,  minutes,  and  seconds,  °,  ',  ",  have  turned  past 
the  microscopes.  In  the  same  room  with  the  meridian- 
circle  and  a  few  feet  south  of  it  there  is  a  small  horizontal 
telescope.  It  has  a  level  which  rests  on  top  of  it,  and  it 
can  be  made  exactly  horizontal.  If  we  point  the  telescope 
of  the  meridian-circle  at  the  small  horizontal  telescope  (see 
the  diagram)  the  meridian-circle  telescope  will  be  horizon- 
Observer's  (  Telescope_of_the  meridian-  Horizontal  telescope 

eye.       \       circle  pointing  south.  pointing  north. 

FIG.  74. — To  DETERMINE  THE  READING  OF  A  MERIDIAN- CIRCLE 

WHEN   IT   IS   POINTED    HORIZONTALLY. 

tal  when  it  sees  directly  down  the  tube  of  the  horizontal 
telescope.  The  circle  must  now  be  read.  Suppose  its 
reading  in  °,  ',  "  to  be  H.  This  reading  H  is  called  the 
horizontal  point.  In  practice  it  is  more  usual  to  deter- 


ASTRONOMICAL  INSTRUMENTS.  131 

mine  the  nadir  point  instead  of  the  horizontal  point  H,  but 
it  is  a  little  simpler  for  the  student  to  consider  the  hori- 
zontal point  as  the  starting-point. 


FIG.  75. — THEORY  OF  THE  MERIDIAN  CIRCLE. 

In  the  figure  HR  is  the  observer's  horizon,  Z  his  zenith,  PZR  his  meri- 
dian, P  the  pole,  E  a  point  of  the  equator,  S  and  S'  the  two  points  where  a 
circumpolar  star  crosses  his  meridian. 

When  the  telescope  is  pointed  south,  at  R,  and  is  horizontal,  the 
circle -reading  is  H.  Let  us  suppose  H  is  equal  to  180°  0'  0".  If  the 
telescope  is  pointed  to  Z  the  reading  will  be  90°  0'  0",  because  the 
zenith  is  90°  from  the  horizon.  If  the  telescope  is  pointed  to  the 
point  PI  (the  north  point  of  the  horizon)  the  reading  will  be  0°  0'  0". 
If  it  is  pointed  to  .ZVthe  reading  will  be  270°  0'  0".  We  need  to  know 
the  reading  for  the  polar  point  P,  and  for  the  equator  point  E. 
The  star  Polaris  is  not  exactly  at  the  North  Pole,  though  it  is  near 
it,  and  so  we  have  no  direct  way  of  pointing  at  the  pole.  If  we 
know  the  latitude  of  the  observer  measured  by  the  arc  HP,  and  it  is 
<p,  then  the  polar  reading  P  will  be  0;  and  the  equator  reading 
E  will  be  90°  +  0  (because  the  arc  PE  is  90°). 

If  we  do  not  know  the  latitude  (f>  we  must  point  the  telescope  at 
a  star  S  when  it  is  crossing  the  meridian  and  determine  its  zenith  dis- 
tance Z8\  and  twelve  hours  later  we  must  again  point  the  telescope 
at  the  same  star,  when  it  is  crossing  the  meridian  again  (at  S'},  and 
determine  the  zenith  distance  ZS'.  Then  (as  has  already  been  proved 
on  page  106), 

The  latitude  of  the  observer  =  $  -  90°  -  \z8  +  Z8'\ 


132 


ASTRONOMY. 


Thus,  whether  the  latitude  of  the  observer  is  known  or  unknown, 
we  can  determine  the  reading  of  the  circle  when  the  telescope  is 
pointed  to  any  one  of  the  points  JR,  E,  Z,  P,  H. 

The   latitude   of  the   Lick   Observatory   is  37°  20'  24"  =  (p. 
meridian-circle  would  then  have  the  following  readings: 


Its 


(H\n  the  figure)     = 


0°    0'    0" 

37°  20'  24" 

90°    0'    0" 

127°  20'  24" 

180°    0'    0" 

270°    0'    0" 


For  the  north -point 

"        solar- point        (P  "  )  = 

"        zenith-point     (Z  "  )  = 

"        equator-point  (E  "  )  = 

"         south -point      (R  "  )  = 

nadir- point       (N  "  )  = 

If  the  telescope  was  pointed  to  a  star  8  as  it  crossed  the  meridian, 
and  if  the  circle  reading  for  8  was  57°  40'  36",  the  north-polar  distance 
of  8  would  be  20°  20'  12",  and  its  declination  would  be  69°  39'  48". 
Its  zenith  distance  north  would  be  32°  19'  24". 

Model  of  a  Meridian  circle. — The  student  will  do  well  to  make  a 
simple  model  of  a  meridian-circle  out  of  wood.  Let  him  take  a  piece 
of  wood  (planed  on  all  its  sides)  about  a  foot  long  and  exactly  square, 
and  whittle  the  ends  of  it  till  they  are  nearly  cylindrical.  This  will 
serve  as  the  axis.  Perpendicular  to  the  axis  at  its  middle  point  he 
should  nail  on  a  flat  piece  of  wood,  about  two  feet  long,  to  stand  for 
the  telescope.  One  end  of  this  last  piece  should  be  marked  "  object- 
glass  "  and  the  other  end  "  eyepiece."  One  pasteboard  circle  8  inches 
in  diameter  should  be  prepared  and  a  paper  circle  divided  to  30' 
(see  page  117)  should  be  neatly  fastened  to  this.  A  square  hole 
should  be  cut  in  the  circle,  exactly  at  its  centre,  and  the  circle  fitted 
to  the  axis  and  fastened  securely  to  it.  Two  wooden  boxes  at  the 
right  distance  apart  will  serve  for  piers.  On  the  top  of  the  piers  Ys, 
sawed  out  of  wood,  must  be  fastened  to  receive  the  pivots  of  the 


FIG.  76. — Ys  OP  A  MERIDIAN-CIRCLE. 


ASTRONOMICAL  INSTRUMENTS.  133 

The  line  joining  the  Ys  should  be  east  and  west.  A  pointer 
must  be  fastened  to  the  pier,  so  that  it  will  just  touch  the  divisions  of 
the  circle  as  they  are  moved  past  it.  It  will  be  convenient  to  make 
this  pointer  of  rather  stiff  copper  wire  bent  to  the  proper  shape  and 
filed  to  a  point  at  the  index  end.  With  a  model  of  this  sort  the 
whole  process  of  observing  with  the  meridian-circle  will  be  very 
clear. 

The  telescope  of  a  transit-instrument  or  of  a  meridian- 
circle  can  only  move  in  one  plane,  namely  in  the  plane  of 
the  celestial  meridian.  As  the  axis  is  turned  the  telescope 
traces  out  the  celestial  meridian  in  the  sky.  Stars  can 
only  be  seen  with  these  instruments  at  the  moments  when 
they  are  crossing  the  meridian  of  the  observer.  For  a 
couple  of  minutes  at  that  time  a  star  is  seen  moving  across 
the  field  of  view  of  the  telescope.  For  the  rest  of  the  24 
hours  (until  the  next  transit)  the  star  cannot  be  seen. 
This  arrangement  is  convenient  if  the  object  is  to  deter- 
mine the  star's  position — its  right-ascension  and  its  decli- 
nation. It  is  very  inconvenient  if  we  desire  to  examine  the 
star  (or  planet)  carefully  to  determine  whether  it  is  a 
double  star,  whether  it  is  surrounded  by  a  nebula,  whether 
its  brightness  is  changing,  and  so  on.  Comets,  for  ex- 
ample, are  very  seldom  seen  far  away  from  the  Sun  and 
therefore  are  seldom  on  the  meridian  during  the  dark 
hours.  Hence  they  are  not  often  observable  by  transit-in- 
struments. 

Equatorial  Mountings  for  Telescopes. — For  such  careful 
examinations  of  the  physical  appearances  of  stars  and 
comets  we  need  to  have  the  telescope  mounted  on  a  stand 
so  contrived  that  we  can  keep  the  star  in  the  field  of  view 
of  the  telescope  for  hours  at  a  time.  We  wish  to  be  able 
to  point  at  a  star  when  it  is  rising  in  the  east  and  to  follow 
it  as  long  as  it  is  above  the  horizon,  if  desirable.  A  mount- 
ing for  a  telescope  that  will  permit  it  to  be  pointed  to  any 
star  above  the  horizon  is  called  an  equatorial  mounting. 
Before  we  describe  the  forms  of  such  mountings  that  are 


134  ASTRONOMY. 

actually  in  use  let  us  see  if  we  can  make  the  principles  on 
which  they  must  be  devised  clear. 

Suppose  we  had  a  very  large  globe  like  the  one  shown  in 
Fig.  44  bis.  Suppose  the  observer  and  the  eye  piece  of  the 
telescope  were  in  the  centre  of  such  a  globe  and  that  the 
object-glass  was  set  in  a  hole  cut  through  the  surface  of  the 
globe  at  some  point  (any  point)  of  the  equator.  It  is  clear 
that  the  observer  could  see  any  star  in  the  equator  so  long 
as  it  was  above  the  horizon,  because  he  would  simply  have 
to  turn  the  globe  (and  the  telescope  with  it)  until  it 
pointed  to  the  star  and  then  to  move  the  globe  slowly  to 
the  west  so  as  to  follow  the  star  as  it  moved  from  rising 
towards  setting.  Such  a  mounting  as  this  would  do  for  a 
star  in  the  equator  and  for  no  other  star;  but  it  would  do 
for  all  stars  in  the  equator. 

If  the  object-glass  were  placed  at  some  point  (any 
point)  in  the  parallel  of  15°  north  declination,  then  all  stars 
in  that  parallel  could  be  viewed  so  long  as  they  were  above 
the  horizon  by  rotating  the  globe,  as  before,  about  its  axis 
that  points  to  the  north  pole.  The  same  thing  would  be 
true  for  stars  on  the  other  parallels  of  30°,  45°,  60°.  It  is 
plain  that  the  mounting  we  want  must  have  a  polar  axis 
like  that  of  the  globe,  so  that  when  the  telescope  is  once 
pointed  at  a  star  that  star  can  be  kept  in  view  from  its 
rising  to  its  setting  by  simply  rotating  the  polar  axis.  It  is 
also  plain  that  the  desired  mounting  must  be  so  contrived 
that  the  telescope  can  be  set  to  any  and  every  declination. 
Such  a  mounting  would  be  used : 

1st.  By  setting  the  telescope  to  the  declination  of  the 
star  we  wished  to  examine: 

3d.  By  following  that  star  as  long  as  we  pleased  by  ro- 
tating the  mounting  about  its  polar  axis. 

If  OP  in  Fig.  77  were  the  polar  axis  of  the  telescope 
and  if  the  telescope  were  set  on  the  stars  A,  B,  (7,  />,  in  suc- 
cession, these  stars  could  be  followed  from  rising  to  setting. 


FIG.    780.  —  THE    36-iNCH    REFRACTOR    OF    THE    LICK   OBSERVATORY    OF    THE 
UNIVERSITY    OF    CALIFORNIA, 


ASTRONOMICAL  INSTRUMENTS.  137 

The  lines  drawn  in  the  different  cones  A,  B,  C,  D,  represent 
different  positions  of  the  telescope.  The  circles  A,  B,  C,  D, 
are  different  parallels  of  declination.  Suppose  then  that  (in 
the  diagram  Figure  78)  TT  is  a  telescope  mounted  on  an 
axis  DL  so  that  TT  can  be  revolved  about  the  axis  DL  so 
as  to  point  to  any  declination;  and  further  suppose  that 
DL  and  TT  together  can  be  rotated  about  the  axis  SN 
which  is  pointed  to  the  north  pole  of  the  heavens. 

The  large  pictures  (Figs.  78#,  80,  81)  show  a  telescope 
mounted  as  in  the  diagram  (Fig.  78).  The  telescope  is 
parallel  to  the  polar  axis. 

If  we  moved  the  upper  end  of  the  telescope  TT  towards 
the  east  to  point  at  another  star  in  another  declination 
such  a  telescope  would  look  as  in  Fig.  81.  If  we  moved  the 
upper  end  of  the  telescope  TT  towards  the  south  to  point 
at  another  star  such  a  telescope  would  look  as  in  Figure 
78$,  where  the  tube  is  pointing  towards  a  star  south  of  the 
zenith,  but  north  of  the  equator  and  not  very  far  from  the 
meridian.  In  the  figure  (78<?)  the  polar  axis  (on  top  of 
the  pier)  is  pointing  to  the  north  pole  of  the  heavens.  The 
north  end  of  the  axis  is  the  highest.  The  declination  axis 
is  fastened  to  the  end  of  the  polar  axis,  and  the  telescope 
is  fastened  to  one  end  of  the  declination  axis.  By  taking 
hold  of  the  eye-end  of  the  telescope  it  can  be  pointed  to 
any  desired  declination  whatever — it  can  be  made  to  point 
south  (horizontally),  to  the  zenith  (vertically),  or  to  the 
pole  (as  in  Fig.  80).  After  it  is  pointed  to  the  desired 
declination  the  polar  axis  can  be  rotated  in  its  bearings 
(about  the  line  N8  in  figure  78)  so  that  the  telescope 
sees  the  desired  star.  The  star  can  be  followed  from  ris- 
ing to  setting  by  slowly  rotating  the  telescope  and  declina- 
tion axis  (together)  towards  the  west. 

If  we  point  such  a  telescope  to  a  star  when  it  is  rising  (doing  this 
by  rotating  the  telescope  first  about  its  declination  axis  and  then 
about  the  polar  axis),  we  can,  by  simply  rotating  the  whole  apparatus 


138 


ASTRONOMY. 


on  the  polar  axis,  cause  the  telescope  to  trace  out  on  the  celestial 
sphere  the  apparent  diurnal  path  which  this  star  will  follow  from 
rising  to  setting.  In  most  telescopes  of  the  sort  a  driving-clock  is 
arranged  to  turn  the  telescope  round  the  polar  axis  at  the  same  rate 
at  which  the  earth  itself  turns  about  its  own  axis  of  rotation — at  the 
rate  at  which  all  stars  move  from  rising  to  setting.  Hence  such  a 
telescope  once  pointed  at  a  star  will  continue  to  point  at  it  so  long  as 
the  driving-clock  is  in  operation,  thus  enabling  the  astronomer  to 


SOUTH 


NORTH 


FIG.  79.— A  SMALL  EQUATORIAL  TELESCOPE  MOUNTED  ON  A 
PORTABLE  STAND. 


make  an  examination  or  observation  of  it  for  as  long  a  time  as  is  re- 
quired. If  we  place  a  photographic  plate  in  the  focus  of  a  suitable 
objective  mounted  equatorially  we  can  obtain  a  long-exposure  picture 
of  the  star-groups  to  which  it  is  directed,  and  so  on. 

The  student  should  make  a  model  of  the  essential  parts  of  an 
equatorial  mounting  out  of  wood.  The  model  should  have  a  polar 
axis  NS  capable  of  being  turned  round  tbe  line  NS;  a  declination 


ASTRONOMICAL  INSTRUMENTS. 


80.— AN  EQUATORIAL   TELESCOPE    POINTED  TOWARDS   THE 
POLE. 


140 


ASTRONOMY. 


FIG.  81.— AN    EQUATORIAL  TELESCOPE  POINTED   AT  A  STAB  IN 
THE  NORTH-EASTERN  REGION  OF  THE  SKY 


ASTRONOMICAL  INSTRUMENTS. 


141 


axis  DL  capable  of  being  turned  round  the  head  of  the  polar  axis  N; 
a  long  stick  TT  to  stand  for  a  telescope  (mark  the  object-glass  end  of 
it).  The  whole  should  be  mounted  on  a  box  so  that  N8  lies  in  a 
north  and  south  line,  and  so  that  the  line  NS  makes  an  angle  with 
the  horizon  equal  to  the  latitude  of  the  observer.  A  surveyor's 
theodolite  becomes  an  equatorial  when  its  horizontal  circle  is  tilted 
up  into  the  plane  of  the  celestial  equator. 


FIG.  82. — THE  MICROMETER. 

An  apparatus  used  in  connection  with  a  telescope  for  measuring  small 
angular  distances. 

The  Micrometer. — A  telescope  on  an  equatorial  mount- 
ing is  very  suitable  for  long-continued  observations,  such 
as  the  examination  of  the  surface  of  a  planet  during  the 
greater  part  of  a  night,  but  in  order  to  fully  utilize  it, 
some  means  of  measuring  must  be  provided.  The  equa- 
torial cannot  be  used  to  measure  large  arcs  with  exactness 
— such  an  arc  as  the  difference  of  declination  of  two  stars 
several  degrees  apart.  When  it  is  provided  with  a 
micrometer  it  is  exactly  fitted  to  measure  small  distances 
with  great  precision — such  a  distance  as  that  between  two 
stars  separated  by  a  few  minutes  of  arc,  for  example. 

The  principle  of  the  micrometer  is  illustrated  in  figure  82.  A 
metal  box  is  fitted  with  two  slides  b  and  c  and  with  two  accurate 
screws  A  and  J5.  The  screw  A  has  a.  head  divided  into  100  parts. 
A  hole  is  cut  in  each  of  the  slides.  A  spider-line,  n,  is  stretched 
across  the  hole  in  the  slide  moved  by  the  screw  A,  and  a  spider-line 
m  is  stretched  across  the  hole  in  the  slide  moved  by  the  screw  B. 


142 


ASTRONOMY. 


The  micrometer  is  fastened  to  the  end  of  the  telescope,  at  right 
angles  to  its  axis,  so  that  the  lines  m  and  n  are  in  the  focus  of  the 
telescope,  thus  : 


FIG.  83. 

OP  is  the  object-glass  of  a  telescope  whose  focus  is  F;  AB  is  the  miprom- 

eter. 

When  the  screw  A  is  moved  the  spider-line  n  moves,  and  the  line 
m  moves  with  the  motion  of  the  screw  B.  The  oval  hole  in  Fig.  82 
represents  the  field  of  view  of  the  telescope.  The  observer  sees  the 
two  spider-lines  m  and  n,  a  fixed  spider-line  at  right  angles  to  them, 
a  comb-scale  at  the  bottom  of  the  field  and  whatever  stars  the  tele- 
scope is  viewing.  One  complete  revolution  of  the  screw  A  moves  the 
line  n  from  one  tooth  of  the  comb-scale  to  the  next  tooth  and  whole 
revolutions  of  A  are  counted  in  this  way.  Fractions  of  a  revolution 
are  counted  on  the  divided  head  of  screw  A  as  its  divisions  move  past 
a  fixed  index  or  pointer. 

Suppose  that  it  is  desired  to  measure  the  distance  between  two 
stars  S  and  jTthat  are  visible  in  the  field  of  view.  During  these 
measures  the  telescope  is  driven  by  the  clock  so  as  to  follow  the  stars 
as  they  move  from  rising  towards  setting. 


FIG.  84. 


The  micrometer  is  moved  so  that  its  long  fixed  spider-line  passes 
through  8  and  Tihus  : 


B- 


FIG.  85. 


ASTRONOMICAL  INSTRUMENTS. 


143 


The  lines  m  and  n  will  appear  as  in  the  figure  85.  The  screw  B  is 
then  moved  until  the  line  m  passes  through  S  and  the  screw  A  is 
moved  till  the  line  n  passes  through  T,  thus  : 


1 1 


FIG.  86. 

The  "reading"  of  the  screw  A  is  then  taken.  Suppose  it  to  be  21 
whole  revolutions  (read  on  the  comb-scale)  and  ^  of  a  revolution 
(read  on  the  divided  head — the  mark  57  being  opposite  to  the  index). 
The  screw  A  is  then  moved  (B  remaining  as  before)  until  the  line  n 
exactly  coincides  with  the  line  m,  and  a  second  "reading"  of  A  is 
made.  Suppose  it  to  be  9  whole  revolutions  (from  the  scale)  and 
T^  (from  the  index).  The  distance  between  the  two  stars  8  and 
T  is  evidently  ST  =  21»\57  -  9r.33  =  12r.24.  If  one  whole  revolu- 
tion of  the  screw  is  known  and  equal  to  11". 07  then  the  distance  ST 
=  12.24  X  11.07  =  135".50. 

When  the  value  of  one  revolution  of  the  screw  is  known  in  sec- 
onds of  arc  all  distances  measured  in  revolutions  and  parts  can  be 
reduced  to  arc.  The  value  of  one  revolution  in  ore  is  determined 
once  for  all  by  placing  the  lines  m  and  n  perpendicular  to  the  direc- 
tion of  the  diurnal  motion  of  a  star  and  at  a  known  distance — say  50 
revolutions — apart,  thus: 

m 


FIG.  87. 


If  the  telescope  is  kept  in  a  fixed  position  the  star,  by  its  diurnal 
motion,  will  move  across  the  field  of  view  in  the  direction  of  the 
arrow.  The  exact  times  of  its  transits  over  n  and  m  are  observed. 


144  ASTRONOMY. 

Suppose  that  it  requires  6m  9.80  of  sidereal  time  to  pass  from  the  line 
n  to  the  line  m. 

6m  9"  =  369"  =  553". 5  because  I8  =  15"  (see  page  84). 

Fifty  revolutions  of  the  screw  =  533". 5,  therefore,  and  1  revolu- 
tion =  11".07. 

The  relative  position  of  two  stars  A  and  B  is  not  completely  de- 
fined when  we  know  their  distance  apart  and  nothing  more.  We 
need  to  know  the  angle  that  the  line  joining  them  makes  with  the 
celestial  meridian  (or  with  the  parallel).  To  determine  this  the  microm- 
eter is  attached  to  a  position- circle,  so  that  the  micrometer-box  can 
be  rotated  in  a  plane  perpendicular  to  the  axis  of  the  telescope.  To 
measure  the  position-angle  of  two  stars  the  telescope  is  kept  in  a  fixed 

position  and  the  micrometer-box 
is  turned  until  one  of  the  stars 
moves  by  its  diurnal  motion 
along  the  spider-line  m.  The 
circle  is  then  "read."  Suppose 
its  "reading"  to  be  90°.  The 
direction  of  the  parallel  (EW)  is 
then  90°  to  270°  ;  of  the  celestial 
meridian  (2?8)  0°  to  180°.  The 
telescope  is  then  pointed  at  A 
and  moved  by  the  driving  clock 
so  that  A  remains  at  the  middle 
of  the  field.  The  micrometer-box 
is  turned  until  the  spider-line  m 
passes  through  the  two  stars  A 
and  B  (see  the  figure)  and  the 
circle  is  again  read.  Suppose 
FIG.  88.— MEASUREMENT  OF  THE  the  reading  to  be  46°.  This  is 
POSITION  ANGLE  OF  Two  the  measure  of  the  angle  NAB 
STARS  A  AND  B.  _0f  tjje  angie  that  the  line  join- 

ing the  two  stars  makes  with  the  celestial  meridian  passing  through 
A.    When  we  know  the  position- angle  and  the  distance  of  two  stars 
we  know  all  that  can  .be  known  about  their  relative  situation. 
1 he  diameters  of  planets  can  be  measured  with  the  micrometer. 
Photography. — If  we  put  a  photographic  plate  in  the  focus  of  the 
telescope  instead  of  a  micrometer,  and   if  we  give  the   proper  ex- 
posure (the  telescope  being  moved  by  the   driving-clock)  we  shall 
have  on  the  plate  a  photograph  of  all  the  stars  in  the  field. 


ASTRONOMICAL  INSTRUMENTS.  145 

If  we  stop  the  clock  and  allow  a  star  to  move  by  its  diurnal  motion 
across  part  of  the  field  of  view  it  will  leave  a  "trail"  from  the 


FIG.  89. 

east  to  the  west  side  of  the  plate.  After  the  plate  is  developed, 
we  shall  have  a  map  of  all  the  stars  and  can  measure  their 

W<  --  —  E 

position-angles  one  from  another,  at  leisure,  and  in  the  daytime. 
Their  distance  apart  can  be  measured  in  inches  and  fractions  of  an 
inch.  The  value  of  one  inch  on  the  plate  expressed  in  seconds 
of  arc  can  be  determined  once  for  all  by  observing  transits  of  a  star 
over  two  pencil  lines  ruled  on  a  ground-glass  plate  in  the  focus  one 
inch  apart.  It  is  clear  that  a  photographic  plate  will  give  us  first, 
a  map  of  all  the  stars  in  the  field  ;  second,  the  means  of  measuring 
their  precise  relative  positions  just  as  measures  with  the  micrometer 
will  do.  One  great  advantage  of  the  photographic  method  over 
visual  measures  with  the  micrometer  is  that  the  plate  gives  a  per- 
manent record,  so  that  the  actual  micrometric  measurements  can  be 
made  at  leisure  and  repeated  as  often  as  necessary.  Another  marked 
advantage  is  that  many  pairs  of  stars  are  photographed  at  one  ex- 
posure, whereas  only  one  pair  can  be  observed  at  one  time  by  the 
eye. 

Celestial  Photography.—  Photographs  of  the  Sun,  Moon,  Planets, 
Stars,  Comets,  and  Nebulae  can  be  made  with  telescopes  specially  con- 
structed for  photography,  and  these  photographs  can  be  subsequently 
studied  under  microscopes,  just  as  if  the  object  itself  were  visible. 
The  intervals  of  clear  sky  can  be  utilized  to  obtain  the  photographs, 
and  they  can  be  measured  when  the  sky  is  cloudy.  A  great  saving 
of  time  is  thus  practicable.  A  second  great  advantage  of  the  photo- 
graphic plate  in  Astronomy  is  that  the  exposures  can  be  made  as 
long  as  desired.  Objects  can  be  registered  in  this  way  that  are  too 
faint  to  be  seen  with  the  eye  using  the  same  telescope.  The  eye  SQOQ 


146 


ASTRONOMY. 


becomes  fatigued  with  the  extreme  attention  required  for  astronomi- 
cal observing.  The  photographic  plate  is  not  subject  to  fatigue.  It 
has  certain  disadvantages  that  need  not  be  discussed  here,  and  the 
plate  will  never  supersede  the  eye.  On  the  other  hand,  it  Las 
already  been  of  immense  importance  in  Practical  Astronomy  and  is 
destined  to  be  employed  in  many  new  ways.  Some  of  its  applications 
are  mentioned  in  Part  II.  of  this  book. 

The  Sextant. — Tiie  sextant  is  a  portable  instrument   universally 


FIG.  90.— THE  SEXTANT. 
The  radius  of  its  divided  circle  is  usually  from  6  to  10  inches. 

used  by  navigators  at  sea.  It  was  invented  by  SIR  ISAAC  NEWTON, 
and  quite  independently  by  THOMAS  GODFREY,  a  sea-captain  of 
Philadelphia.  The  figure  shows  its  general  appearance.  Its  pur- 
pose is  to  measure  the  altitude  of  a  star  (or  of.  the  Sun),  It  consists 


ASTRONOMICAL  INSTRUMENTS.  147 

essentially  of  a  divided  circle;  of  a  movable  index  arm  SM which 
carries  a  mirror  M  (called  the  index-glass)  firmly  fastened  to  it ;  of 
another  mirror  m  (called  the  horizon-glass)  fastened  to  the  frame  of 
the  instrument  ;  and  of  a  small  telescope  E.  It  is  held  by  a  handle 
H.  When  altitudes  are  measured,  the  plane  of  the  instrument  is 
vertical. 

The  instrument  is  used  daily  at  sea  to  measure  the  altitude  of  the 
Sun.  The  chronometer-time  at  which  the  altitude  is  measured  is 
noted.  The  method  of  making  the  observation  is  to  point  the 
telescope  E  at  the  sea-horizon,  which  will  appear  like  a  horizontal 
line  across  its  field  of  view,  thus  : 


The  rays  from  the  Sun  strike  the  index-glass  A  (or  M  in  Fig.  90), 
and  are  reflected  from  it.  By  moving  the  index-arm  (the  glass 
moves  with  it)  the  reflected  rays  from  the  Sun  (AB)  may  be  made  to 


FIG  91.— THEORY  OP  THE  SEXTANT. 

fall  on  the  horizon-glass  B  (or  m  in  Fig.  90).     When  the  index-arm 
has  been  moved  so  that  the  image  of  the  Sun  (Q)  appears  to  touch 

the  horizon  -  the  index-arm  reads  the  altitude  of  the 

Sun  on  the  divided  circle. 

The  altitude  of  the  Sun  is  also  measured  daily  at  apparent  noon,  that 
is  when  the  Sun  is  highest,  by  every  navigator  to  obtain  his  latitude. 

In  the  figure  Z'  is  an  observer  on  the  Earth  CP'Z'Q',  Z  is  his 
zenith,  EH  his  horizon,  P  is  the  celestial  pole,  PZH  his  celestial 
meridian,  <J  a  point  of  the  celestial  equator.  $  is  the  Sun  on  hia 


148  ASTRONOMY. 

meridian.  The  altitude  of  the  Sun  HS  is  measured  by  the  sextant. 
90°  —  H8  =  ZS,  and  Z8  is  thus  a  known  arc.  The  declination  of  the 
Sun  at  that  instant  is  QS.  It  is  a  known  quantity  because  it  can  be 
taken  from  tables  in  the  Nautical  Almanac  that  have  been  calculated 

beforehand.  QZ  =  the  declina- 
tion of  the  observer's  zenith  =  his 
latitude  =  ZS-\-  QS  =  the  sum  of 
two  known  arcs.  If  the  Sun  is  on 
the  meridian  north  of  tie  observ- 
er's zenith,  as  it  may  be  in  certain 
latitudes,  QZ  =t\ie  observer's  lati- 
tude =  QS'  —  ZS'=  the  Sun's  decli- 
nation (a  known  quantity)  minus 
the  Sun's  zenith  distance  (which 

FIG.  93.-THE  LATITUDE  OF  AN  |s  .kno,wn  *s  600n  as  Bff'  *'  al,tl- 

OBSERVER  DETERMINED   BY  tudf'  ***  ^  ™*sa™d,  ™  h  *''« 

,.  ,,  sextant).     Thus  the  ship  s  latitude 

MEASURING    THE    MERIDIAN  .    ,  A       .     , 

is  determined. 

ALTITUDE  OF  THE  SUN.  mi      ....          .,  .,     0 

The  altitude  of  the  Sun  is  meas- 
ured daily  in  the  morning  (or  afternoon,  or  both)  to  determine  the 
ship's  longitude,  or  rather  to  determine  the  local  mean  time  of  the 
ship's  position.  If  we  know  that  the  local  mean  time  of  the  ship  is 
T &t  the  instant  that  the  Greenwich  time  is  O  the  west  longitude  of 
the  ship  will  be  O  —  7'(=the  difference  of  the  simultaneous  local 
times).  The  Greenwich  time  is  always  known,  on  the  ship,  from  the 
dial  of  the  Greenwich  chronometer  that  she  carries.  The  local  time 
of  the  ship  is  calculated  from  the  triangle  ZPA  as  soon  as  the  Sun's 
altitude  has  been  measured. 

In  figure  93  PZS  is  the  celestial  sphere,  0  the  place  of  the  Earth, 
Zihe  zenith  of  an  observer,  NS  his  horizon,  ZJ7his  east  point,  A  the 
place  of  the  Sun  in  the  afternoon,  BA  the  Sun's  declination,  PA  the 
Sun's  north  polar  distance,  OA  the  Sun's  altitude,  ZA  the  Sun's 
zenith  distance.  The  angle  ZPA  is  the  local  apparent  solar  time 
because  it  is  the  hour-angle  of  the  Sun  (see  page  90).  We  wish  to 
determine  ZPA.  In  the  triangle  ZPA,  PA  is  known  (it  is  90°  minus 
the  Sun's  declination  which  is  given  in  the  Nautical  Almanac} ;  ZP 
is  known  (it  is  90°  minus  the  latitude  PN)  ;  ZA  is  known  (it  is  90° 
minus  the  Sun's  altitude  which  has  been  measured  by  the  sextant). 
Hence  every  part  of  the  triangle  is  known  and  the  angle  ZPA  (ex- 
pressed in  hours,  minutes  and  seconds,  not  in  degrees,  etc.)  corrected 
for  the  difference  between  mean  and  apparent  solar  time  gives  the 
local  time  of  the  ship  =  T<  If  O  is  the  Greenwich  time  (from  the. 


ASTRONOMICAL  INSTRUMENTS.  149 

Greenwich  chronometer)  at  that  instant,  the  ship's  west  longitude  is 
O  —  T,  a  known  quantity. 

Thus  a  little  instrument  that  can  be  held  in  the  hand  enables  the 
navigator  to  determine  his  position  on  the  Earth's  surface  with  con- 
siderable accuracy  and  in  a  very  few  minutes.  Sextant  observations 
at  sea  will  give  the  position  of  a  ship  to  within  a  mile  or  so. 

—  Make  a  sketch  of  the  transit  instrument  and  name  the  impor- 
tant parts— the  telescope,  the  axis,  the  Ys,  the  piers.  When  the  in- 


Fiu.  93  — THE  LOCAL  TIME  OF  AN   OBSERVER   DETERMINED  UY 
MEASURING  THE  ALTITUDE  OF  THE  SUN. 

strument  is  revolved,  what  circle  of  the  celestial  sphere  does  it  trace 
out?  If  a  star  of  known  R.A.  =  A  crosses  the  meridian  at  a  ctock 
time  T,  what  is  the  correction  of  the  clock  ?  If  the  sidereal  clock  is 
correct,  and  a  star  of  unknown  R.A.  crosses  the  meridian  at  a  time 
B,  what  is  the  R.  A.  of  this  star  ? 

Make  a  sketch  of  the  important  parts  of  the  meridian-circle,  and 
name  the  parts.  How  may  the  horizontal-point  H  of  the  circle  be 
determined  ?  Suppose  H  to  be  known,  what  is  the  reading  for  the 
zenith-point  Z?  lor  the  nadir?  Suppose  the  latitude  of  the  observer 
(=  <t>)  to  be  known  also,  what  is  the  reading  for  the  polar  point  Pf 


150  ASTRONOMY. 

for  the  equator-point  E?  Describe  how  a  model  of  a  meridian-circle 
can  be  made.  For  what  purpose  are  transit  instruments  and  merid- 
ian-circles used?  Describe  the  equatorial  mounting  for  telescopes, 
and  say  what  its  advantages  are.  Draw  a  diagram  of  such  a  mount- 
ing. Explain  the  construction  of  a  micrometer.  How  is  it  used  to 
determine  the  angular  distance  of  two  stars — their  position-angle? 
How  is  the  value  of  one  revolution  of  the  micrometer  determined  in 
arc?  Explain  how  a  photograph  of  a  group  of  stars  is  made.  What 
are  some  of  the  advantages  of  photographic  methods  of  observation  Y 
With  the  sextant  the  altitude  of  the  Sun  (or  of  a  star)  can  be  meas- 
ured. How  is  the  latitude  of  a  ship  at  sea  determined  ?  the  longitude 
of  the  ship  ? 

The  Nautical  Almanac.—  The  governments  of  the  United  States, 
Great  Britain,  France,  Germany,  and  other  countries  issue  annually  a 
Nautical  Almanac  for  the  use  of  navigators  and  others.  Copies  of 
the  Nautical  Almanac  can  be  purchased  through  book-dealers.  The 
Almanac  contains  : 

Tables  of  the  R.A.  and  Decl.  of  the  Sun,  Moon,  and  Planets  for 
every  day  in  the  year. 

Tables  of  the  R.  A.  and  Decl.  of  all  the  brighter  stars. 

Tables  of  all  eclipses  of  the  Sun,  Moon,  and  of  the  satellites  of 
Jupiter,  as  well  as  many  other  data  of  importance  to  the  astronomer 
and  the  navigator. 

To  give  the  student  a  better  idea  of  the  Nautical  Almanac  a  sir  all 
portion  of  one  its  pages  for  the  year  1882  is  here  printed.  (See  page 
151.) 

The  third  column  shows  the  R.  A.  of  the  Sun's  centre  at  Green- 
wich mean  noon  of  each  day.  The  fourth  column  shows  the  hourly 
change  of  this  quantity  (9.815  on  Feb.  12).  At  Greenwich  0  hours,  on 
Feb.  12,  the  sun's  R.  A.  was  21h  44m  KK80.  Washington  is  5h  8"' 
(5h.13)  west  of  Greenwich.  At  Washington  mean  noon,  on  the  12th, 
the  Greenwich  mean  time  was  5h.l3.  9.815  X  5.13  is  50*.35.  This 
is  to  be  added  since  the  R.  A.  is  increasing.  The  sun's  R.  A.  at 
Washington  mean  noon,  on  Feb.  12,  is  therefore  21h  45ra  1M5.  A 
similar  process  will  give  the  sun's  declination  for  Washington  mean 
noon.  In  the  same  manner,  the  R.  A.  and  Dec.  of  the  sun  for  any 
place  whose  longitude  is  known  can  be  found. 

The  column  "Equation  of  Time  "  gives  the  quantity  to  be  sub- 
tracted from  the  Greenwich  mean  solar  time  to  obtain  the  Green- 
wich apparent  solar  time  (see  page  90).  Thus,  for  Feb.  1,  the 
Greenwich  mean  time  of  Greenwich  mean  noon  is  0"  0'"  0".  The 


ASTRONOMICAL  INSTRUMENTS. 


151 


true  sun  crossed  the  Greenwich  meridian  (apparent  noon)  13m  51s.  34 
earlier  than  this,  that  is  at  23b  46m  08s. 66  on  the  preceding  day  ; 
i.e.  Jan.  31.  Having  the  apparent  solar-time  by  observation  (see 
page  148)  the  mean  solar  time  can  be  found  from  this  table. 

Again,  when  it  was  Oh  Om  0s  of  Greenwich  mean  time  on  Feb.  10, 
it  was  21h  21m  50s. 70  of  Greenwich  local  sidereal  time  (see  the  last 


FEBRUARY,  1882— AT  GREENWICH  MEAN  NOON. 


Day 

a 

*      ; 

THE  SUN'S 

Equation 
of  time 

b 

X) 

Sidereal 
time 

of 

to  be 

h 

or  right- 

tlie 
week. 

I1 

Apparent 
right- 
ascension. 

Diff. 
for  1 
hour. 

Apparent 
declination. 

Diff. 
for  1 
hour. 

substracted 
from 
mean 
time. 

•8 
d 
S 

ascension 
of 
mean  sun. 

H.     M.        S. 

s. 

0             /              // 

// 

M.         S. 

s. 

H.    M.     S. 

Wed. 

1 

21     0    13.04 

101.75 

S  17      2    22.4 

+42.82 

13    51.34 

0.318 

20  46  21.70 

Thur. 

2 

21     4    16.84 

10.141 

16    45      5.4 

43.57 

13    58.58 

0.284 

20  50  18.26 

Fri. 

3 

21    8    19.82 

10.107 

16    27    30.9 

44.30 

14      5.01 

0.250 

20  54  14.81 

Sat. 

4 

21  12    21.98 

10.073 

16      9    39.2 

+44.99 

14     10.61 

0.216 

20  58  11.37 

Sun. 

5 

21  16    23.33 

10.040 

15    51    30.8 

45.69 

14    15.41 

0.183 

21    2    7.92 

Mon. 

6 

21  20    23.88 

10.007 

15    33      6.1 

46.36 

14    19.40 

0.150 

21    6    4.48 

Tues. 

7 

21  24    23.63 

9.974 

15     14    25.4 

+47.03 

14    22.60 

0.117 

21  10     1.03 

Wed. 

8 

21  28    22.60 

9.941 

14    55    29.1 

47.66 

14    25.01 

0.084 

21   13  57.59 

Thur. 

y 

21  32    20.79 

9.909 

14    36    17.7 

48.28 

14    26.65 

0.052 

21  17  54.14 

Fn. 

10 

21  36    18.21 

9.877 

14    16    51.6 

48.88 

14    27.51 

0.020 

21  21  50.70 

Sat. 

n 

21  40    14.88 

9.846 

13    57     11.2 

49.47 

14    27.63 

0.011 

21  25  47.25 

Sun. 

12 

21  44    10.80 

9.815 

13    37    16.9 

50.03 

14    26.99 

0.042 

21  29  43.81 

column  of  the  table).  Having  the  sidereal  time  by  observation  (see 
page  127),  the  corresponding  mean  solar  time  can  be  found  from  this 
table. 

How  to  Establish  a  True  North  and  South  Line.— In  order  to  set  the 
hands  of  a  sidereal  timepiece  correctly  we  must  make  them  indicate 
the  hours,  minutes,  and  seconds  of  any  star's  right-ascension  at  the 
instant  that  star  is  crossing  the  observer's  meridian.  In  order  to 
make  the  timepiece  keep  sidereal  time  correctly  we  must  regulate 
it  so  that  the  hands  go  through  24°  Ora  0s  in  the  interval  between  two 
successive  transits  of  the  same  star  across  the  meridian.  To  make 
these  observations,  we  need  to  know  the  direction  of  the  meridian, 
and  to  mark  it  permanently. 

For  students  who  cannot  own  a  transit  instrument  it  is  convenient 
to  mark  the  meridian  by  two  plumb-lines,  A  and  B,  one  due  north  of 
the  other,  thus: 


152 


ASTRONOMY. 


B 


P 

A 


FIG.  94. 


The  plumb-lines  can  be  made  out  of  good  fishing-line  ;  the  plumb- 
bobs  out  of  bits  of  lead.  To  prevent  them  from  swinging  in  the  wind 
it  is  a  good  plan  to  keep  the  bobs  immersed  in  pails  of  water.  The 
lines  can  be  suspended  from  nails  driven  into  walls,  trees,  etc.  The 
meridian-line  should  be  marked  in  a  place  where  a  good  view  of 
the  whole  meridian  from  north  to  south  can  be  commanded. 

The  problem  is  to  place  the  plumb-lines  in  a  true  north  and  south 
line.  There  are  several  ways  of  doing  this.  The  following  process 


FIG.  95.  —  URSA  MA  JOE, 
Zeta  (£)  Ursro  majoris  is  the  middle  star  of  the  handle  of  the  Dipper. 


is  as  simple  as  any.  Mark  on  the  ground  a  line  in  the  direction  of  the 
needle  of  a  common  compass.  This  will  be  approximately  north  and 
south.  At  the  north  end  of  this  line  choose  a  place  for  the  northern 
plumb-line  A  and  hang  it  there.  Ten  or  fifteen  feet  south  of  A  sus- 
pend the  second  plumb-bob  B  from  a  framework  of  wood  that  can 
be  moved  east  or  west,  if  necessary.  A  is  always  to  hang  in  the 
place  first  chosen.  B  is  to  be  moved  east  or  west  until  the  right 
place  is  found  and  then  it  is  to  remain  there  always.  The  line  join- 


ASTRONOMICAL  INSTRUMENTS.  153 

ing  A  and  B  (after  B  is  placed  correctly)  is  the  meridian  line  of  the 
observer. 

The  plumb-line  B  is  placed  correctly  when  both  plumb-lines  seem 
to  pass  through  the  two  stars  Polaris  and  Zeta  (C)  Ursce  majoris  at  the 
same  time. 

The  right-ascensions  of  these  two  stars  differ  by  12  hours.  When 
Polaris  is  crossing  the  meridian  from  east  to  west  (upper  culmina- 
tion) C  Ursa  majoris  is  crossing  the  meridian  from  west  to  east  (lower 
culmination).  A  line  joining  them  at  this  instant  is  a 
celestial  meridian.  If  we  move  the  plumb-line  B  until 
both  plumb-lines  A  and  B  pass  through  both  stars  then  the 
line  joining  A  and  B  must  be  in  the  plane  of  the  celestial 
meridian. 

The  stars  will  be  approaching  their  culminations 

about  11  P.M.  Oct.  20,  about  8  P.M.  Dec.  5, 

"     10     "     Nov.  5,  "     7     "     Dec.  20, 

9     "     Nov.  20,  "     6     "     Jan.  5, 

about  5  P.M.  Jan.  20, 
and  these  are  the  hours  to  prepare  to  observe  them. 

The  observation  consists  in  moving  the  support  of  the 
plumb-line  B  (the  southern  plumb-line)  slowly  and  gently 
east  or  west  until  both  stars  seem  to  be  on  the  two  plumb- 
lines  at  the  same  time,  as  in  Fig.  96.     When  they  are  so 
let  both  plumb-lines  rest,  and  see  if  the  stars  stay  on  the  ™        Q« 
two  lines  for  a  few  minutes.     If  they  do,  both  lines  are 
in   the  right  position.     If  they  do  not,  move  the  southern  plumb- 
line  B  slightly.     After  the  plumb-line  B  has  been  put  in  the  right 
position  its  place  must  be  marked;  and  tbe  next  morning  its  nail  can 
be  permanently  fixed.     It  will  be  well  to  test  the  meridian-line,  so 
determined,  by  another  night's  observations.     Finally,  a  meridian- 
line  can  be  established  by  this  process;  and  whenever  the  observer 
wishes  he  can  observe  the  transit  of  any  celestial  body  over  the  two 
plumb-lines  and  note  the  hour,  minute,  and  second  by  his  sidereal 
time  piece.*     In  order  to  see  the  plumb-lines  in  a  dark  night  he 
should  chalk  them  well,  or  paint  them  white.     If  this  is  not  enough 
they  can  be  illuminated  by  the  light  of  a  lantern  placed  behind  his 
back  (so  as  not  to  interfere  with  his  seeing  the  stars). 

*  A  cheap  watch,  regulated  to  run  on  sidereal  time,  is  a  great  con- 
venience in  making  astronomical  observations. 


CHAPTER   VIII. 

APPARENT  MOTION  OF  THE  SUN  TO  AN  OBSERVER  ON 
THE  EARTH— THE  SEASONS. 

21.  Apparent  Motion  of  the  Sun  to  an  Observer  on 
the  Earth. — Long  before  the  Christian  era  the  ancients 
knew  that  there  were  two  classes  of  bodies  to  be  seen 
in  the  sky.  The  stars — the  first  class — rose  and  set,  to 
be  sure;  but  they  were  always  in  the  same  relative  posi- 
tion. They  kept  their  configurations.  They  were  fixed. 
One  star  did  not  move  away  from  others.  The  stars  of 
Ursa  Major  shown  in  Fig.  1  kept  their  relative  positions — 
their  grouping — century  after  century.  There  was  another 
class  of  celestial  bodies  which  the  ancients  called  planets  or 
wandering  stars.  Some  of  them  (Mercury r,  Venus,  Mars, 
Jupiter,  Saturn)  looked  exactly  like  stars  to  the  naked 
eye,  but  they  moved  among  the  fixed  stars,  sometimes 
being  near  to  one  fixed  star,  then  leaving  it  and  moving 
near  another  star.  You  can  easily  observe  such  motions 
as  these  for  yourself.  Mars  or  Jupiter  moves  among  the 
fixed  stars  with  a  motion  that  is  quite  obvious  if  you  regu- 
larly observe  its  place  (and  make  a  sketch  of  the  stars  near 
by).  The  Moon  moves  quite  rapidly  among  the  stars. 

The  Sun  also  moves  among  the  stars,  but  as  the  stars 
are  not  visible  in  the  daytime,  it  is  necessary  to  observe 
the  Sun  at  sunrise  and  at  sunset  in  order  to  prove  to 
yourself  that  it  is  moving.  The  ancients  understood  this 
fact  very  well  and  they  had  mapped  the  path  of  the  Sun 
among  the  stars  quite  accurately.  You  can  do  the  same 
thing  by  observing  the  Sun  at  sunrise  and  sunset  each 

154 


APPARENT  MOTION  OF  THE  SUN.  155 

day  and  by  marking  down  on  a  celestial  globe,  every  day, 
the  position  of  the  Sun.  If  you  continued  this  process  for 
a  year  you  would  find  that  the  Sun  had  apparently  made  a 
complete  circuit  of  the  heavens. 

If  the  Sun  were  near  to  a  bright  star  on  Jan.  1  (so  that 
the  Sun  and  the  star  rose  and  set  at  the  same  time)  you 
would  see  that  the  Sun  moved  eastwards  so  as  to  set  later 
than  the  star  on  Jan.  2.  It  would  set  still  later  than  the 
star  on  Jan.  3,  and  so  on.  In  July  it  would  set  about 
13  hours  later  than  the  star.  In  half  a  year  the  Sun  has 
moved  away  from  the  star  by  half  the  circuit  of  the 
heavens.  In  the  next  January  the  Sun  would  be  near  the 
same  star  again  so  as  to  set  at  the  same  time  with  it.  The 
Sun  then  has,  in  the  year,  made  a  complete  circuit  of  the 
heavens.  The  ancients  proved  this  and  you  can  prove  it 
for  yourself  if  you  will  give  a  year  to  the  demonstration. 
The  year  is  measured  by  the  time  required  for  the  Sun  to 
make  this  circuit. 

The  explanation  of  the  apparent  motion  of  the  Sun  is  to 
be  found  in  the  real  motion  of  the  Earth.  The  Earth 
moves  round  the  Sun  in  a  nearly  circular  orbit  (path)  and 
completes  one  revolution  in  about  365£  days,  one  year. 

In  Fig.  97  let  8  represent  the  Sun,  ABCD  the  orbit  of 
the  Earth  around  it,  and  EFGH  the  sphere  of  the  fixed 
stars.  This  sphere  is  infinitely  larger  than  the  circle 
ABCD.  Suppose  now  that  1,  2,  3,  4,  5,  6  are  a  number 
of  consecutive  positions  of  the  Earth  in  its  orbit.  A  line 
IS  drawn  from  the  Sun  to  the  Earth  in  any  given  position 
is  called  the  radius-vector  of  the  Earth.  Suppose  this  line 
extended  so  as  to  meet  the  celestial  sphere  in  the  point  1'. 
It  is  evident  that  to  an  observer  on  the  Earth  at  1  the  Sun 
will  appear  projected  on  the  celestial  sphere  at  1';  when 
the  earth  reaches  2  the  Sun  will  appear  at  2',  and  so  on. 
In  other  words,  as  the  Earth  revolves  around  the  Sun,  the 
latter  will  seem  to  perform  a  revolution  among  the  fixed 


156  ASTRONOMY. 

stars.  The  stars  do  not  seem  to  move  because  they  are  at 
such  enormous  distances  that  a  change  of  the  Earth's  place 
from  1  to  6,  or  from  A  to  (7,  makes  almost  no  change  in 
the  direction  of  lines  joining  the  Earth  and  any  star.  In 
space  the  lines  HA,  HC,  HD,  HB  are  almost  (though  not 
quite)  parallel. 


FIG.  97. — THE  ANNUAL  REVOLUTION  OF  THE  EARTH  ABOUT  THE 

SUN,  IN  THE  ORBIT  ABCD. 
The  diameter  of  this  orbit  is  about  186,000,000  miles. 

The  apparent  places  of  the  Sun  (!',  2',  3',  4',  5',  6',  etc.) 
can  be  defined  in  the  sky  by  their  right-ascensions  and 
declinations,  or  by  their  distances  from  the  stars  there 
situated.  The  right-ascensions  and  declinations  of  these 
stars  are  known  (or  if  they  are  not  known  they  can  be 
determined  by  observation). 


APPARENT  MOTION  OF  THE  SUN.  157 

It  is  plain  that  an  observer  on  the  San  would  see  the 
Earth  projected  at  points  on  the  celestial  sphere  exactly 
opposite  to  the  corresponding  points  of  the  Sun's  apparent 
path  viewed  from  the  Earth.  Moreover,  if  the  Earth 
moves  more  rapidly  in  some  portions  of  its  orbit  than  in 
others  (as  it  does)  the  Sun  will  appear  to  move  more  rapidly 


FIG    98. — THE  REVOLUTION  OF  THE  EARTH  IN  ITS  ORBIT  ABOUT 

THE  SUN. 


among  the  stars  in  consequence.  The  two  motions  must 
accurately  correspond  one  with  the  other.  The  apparent 
motion  of  the  Sun  in  the  heavens  is  a  precise  measure  of 
the  real  motion  of  the  Earth  in  its  orbit. 

The  radius-vector  of  the  Earth  (the  line  joining  Earth 
and  Sun)  describes  a  plane  surface  as  the  Earth  moves. 


158  ASTRONOMY. 

In  the  figure  this  is  the  plane  of  the  paper.  In  space  this 
plane  is  called  the  plane  of  the  ecliptic.  This  plane  will 
cut  the  celestial  sphere  in  a  great  circle;  and  the  Sun  will 
appear  to  move  in  this  circle.  The  circle  is  called  the 
ecliptic.  The  plane  of  the  ecliptic  divides  the  celestial 
sphere  into  two  equal  parts.  A  sidereal  year  is  the  interval 
of  time  required  for  the  Sun  to  make  the  circuit  of  the  sky 
from  one  star  hack  to  the  same  star  again ;  or,  it  is  the 
interval  of  time  required  for  the  Earth  to  go  once  around 
its  orbit. 

When  the  earth  is  at  1  in  the  figure  the  Sun  will  appear 
to  be  at  1',  near  some  star,  as  drawn.  Now  by  the  diurnal 
motion  of  the  Earth  the  Sun  is  made  to  rise,  to  culminate, 
and  to  set  successively  to  every  observer  on  the  Earth. 
This  star  being  near  the  Sun  rises,  culminates,  and  sets  with 
him;  it  is  on  the  meridian  of  any  place  at  the  local  noon 
of  that  place  (and  is  therefore  not  visible  except  in  a  tele- 
scope since  we  cannot  see  stars  in  the  daytime  with  the 
naked  eye).  The  star  on  the  right-hand  side  of  the  figure, 
near  the  line  CS1  prolonged,  is  nearly  opposite  to  the  Sun. 
When  the  Sun  is  rising  at  any  place,  that  star  will  be 
setting;  when  the  Sun  is  on  the  meridian  of  the  place,  that 
star  is  on  the  lower  meridian;  when  the  sun  is  setting,  that 
star  is  rising.  It  is  about  180°  from  the  Sun. 

Now  suppose  the  Earth  to  move  to  2.  The  Sun  will  be 
seen  at  2',  near  the  star  there  marked.  2'  is  east  of  1';  the 
Sun  appears  to  move  among  the  stars  (in  consequence  of 
the  earth's  annual  motion)  from  west  to  east.  The  star 
near  2'  will  rise,  culminate,  and  set  with  the  Sun  to  every 
observer  on  the  Earth.  Like  things  are  true  of  the  Sun 
in  each  of  its  successive  apparent  positions  3',  4',  5',  6',  etc. 

The  student  should  here  notice  how  onr  notions  of  the 
direction  East  and  West  have  arisen.  In  the  first  place 
men  noticed  that  the  Sun  rose  in  one  part  of  the  sky 
(which  they  namecl  East)  and  set  iu  another  (West), 


APPARENT  MOTION  OF  THE  SUN.  159 

Secondly,  it  was  found  that  these  risings  and  settings  were 
caused  by  the  daily  rotation  of  the  Earth  on  its  axis  and 
that  if  the  stars  appeared  to  move  from  east  to  west  the 
Earth  must  really  turn  from  west  to  east.  The  Sun 
appears  to  move,  in  consequence  of  the  Earth's  annual 
motion,  from  west  to  east  among  the  stars  (from  1' 
towards  6'  in  the  figure). 

The  Earth  moves  around  its  circle  ABCD  in  the  same 
direction  that  the  Sun  appears  to  move  around  its  circle 
FGHE.  Draw  an  arrow  outside  of  FGHE  parallel  to 
1',  2',  3',  4',  5',  6',  with  the  point  near  6'  and  the  feather 
near  I'.  Draw  another  arrow  outside  of  ABCD  with  the 
point  near  D  and  the  feather  near  G.  These  arrows  are 
parallel.  Hence  the  Earth  moves  in  its  orbit  from  west  to 
east.  Or,  suppose  ABCD  and  FGHE  to  be  two  watch- 
dials  and  8 A  and  8E  to  be  the  hands.  When  8 A  points  to 
the  top  of  its  dial  (ABCD)  its  next  movement  is  towards  the 
left  (in  the  figure).  When  SE  points  to  the  top  of  its  dial 
(FGHE)  its  next  movement  is  towards  the  left,  likewise. 
As  the  Sun  is  observed  to  move  from  west  to  east  among 
the  stars,  the  Earth  must  also  move  from  west  to  east  in 
its  orbit. 

The  apparent  position  of  a  body  as  seen  from  the  Earth 
is  called  its  geocentric  place.  The  apparent  position  of  a 
body  as  seen  from  the  sun  is  called  its  heliocentric  place. 

In  the  last  figure,  suppose  the  Sun  to  be  at  S,  and  the 
Earth  at  4.  4'  is  the  geocentric  place  of  the  Sun,  and  G 
is  the  heliocentric  place  of  the  Earth. 

THE  SUN'S  APPARENT  PATH. 

It  is  evident  that  if  the  apparent  path  of  the  Sun  lay  in 
the  equator,  it  would,  during  the  entire  year,  rise  exactly 
in  the  east  and  set  in  the  west,  and  would  always  cross  the 
meridian  at  the  same  altitude  (see  page  68).  The  days 
would  always  be  twelve  hours  long,  for  the  sa,m§  reason 


160  ASTRONOMY. 

that  a  star  in  the  equator  is  always  twelve  hours  above  the 
horizon  and  twelve  hours  below  it.  But  we  know  that 
this  is  not  the  case.  The  Sun  is  sometimes  north  of  the 
equator  and  sometimes  south  of  it,  and  therefore  it  has  a 
motion  in  declination. 

The  Sun  was  observed  with  a  meridian-circle  and  a 
sidereal  clock  at  the  moment  of  transit  over  the  meridian 
of  Washington  on  March  19,  1879.  Its  position  was  found 
to  be 

Eight-ascension,  23h  55m  23s;  Declination,  0°  30'  south. 

The  observation  was  repeated  on  the  20th  and  following 
days,  and  the  results  were : 

March  20,  E.  A.  23h  59m  2s;  Dec.  0°  6' South. 
"  21,  "  Oh  2m  40s;  "  0°  17'  North. 
"  22,  "  Oh  6m  19s;  "  0°  41'  " 

If  we  lay  these  positions  down  on  a  chart,  we  shall  find 
them  to  be  as  in  Fig.  99,  the  centre  of  the  Sun  being  south 
of  the  equator  in  the  first  two  positions,  and  north  of  it  in 
the  last  two.  Joining  the  successive  positions  by  a  line, 
we  shall  have  a  representation  of  a  small  portion  of  the 
apparent  path  of  the  Sun  on  the  celestial  sphere,  or  of  the 
ecliptic. 

It  is  clear  that  the  Sun  crossed  the  equator  on  the  after- 
noon of  March  20,  1879,  and  therefore  that  the  equator 
and  ecliptic  intersect  at  the  point  where  the  Sun  was  at 
that  time.  This  point  is  called  the  vernal  equinox,  the 
first  word  indicating  the  season,  while  the  second  expresses 
the  equality  of  the  nights  and  days  which  occurs  when  the 
Sun  is  on  the  equator. 

If  similar  observations  are  made  at  any  place  on  the 
Earth  in  any  year  it  will  be  found  that  the  Sun  moves 
along  the  ecliptic  from  the  southern  hemisphere  into  the 
northern  hemisphere  about  March  20  of  each  and  every 
year;  and  the  point  where  the  ecliptic  crosses  the  equator-— 


APPARENT  MOTION  OF  TEE  SUN. 


161 


the  vernal  equinox — can  be  determined  by  observation. 
The  declination  of  this  point  is  zero  (because  it  is  on  the 
equator)  and  its  right-ascension  is  also  zero  (because  right- 
ascensions  are  counted  from  the  vernal  equinox).  From 


FIG.  99.— THE  SUN  CROSSING  THE  EQUATOR. 

March  to  September  the  Sun  is  in  the  northern  hemi- 
sphere. Figs.  49,  50,  51,  52  have  the  ecliptic  marked 
upon  them,  and  the  student  should  point  out  the  places  of 
the  Sun  for  the  beginning  of  each  month  of  the  year  (so 
far  as  is  possible)  on  each  figure.  (See  the  next  paragraph.) 
Here  for  example  are  the  positions  of  the  Sun  for  the  first  day  of 
every  month  of  the  year  1898  at  Greenwich  mean  noon: 


1898  (Jan.    1 
South  \  Feb.    1 
(Mar.    1 
(Apr.    1 
May    1 
June  1 
July    1 
Aug.   1 
(  Sept.  1 

;  Oct.   i 

South  -{Nov.  1 
Dec.    1 


R.  A    = 


Dccl.  = 


North 


18h  49m 
21h  lm 
22b  50m 

Ob43m 

2b  35m 

4b38m 

6b42m 

8b47m 
10h  43m 
12b  31ra 
14h  27m 
16b  31m 

On  June  21,  1898,  the  Sun  had  its  greatest  nortJiern  declination 
=  +  23°  27';  on  December  22,  1898,  the  Sun  had  its  greatest  southern 
declination  =  -  33°  27', 


South   23° 

"       17° 

7° 

North     5° 

"       15° 

22° 

"       23- 
"       18° 

go 

South     3° 

15° 

"       22° 


162 


ASTRONOMY. 


If  the  right-ascensions  and 
declinations  of  the  Sun  dur- 
ing the  months  from  March 
to  September  are  laid  down 
on  a  map  we  shall  have  a 
diagram  like  Fig.  100.  The 
straight  line  represents  the 
celestial  equator.  The  vernal 
equinox  is  at  the  right-hand 
side  of  the  picture.  The 
right-ascension  of  the  vernal 
equinox  is  zero,  and  the  hours 
of  right-ascension  are  marked 
I,  II,  ...  X,  XL  These 
numbers  increase  as  you  go 
eastwards;  hence  the  point 
XI  is  east  of  the  point  II. 

The  Sun  crosses  the  equator 
(going  northwards)  at  the 
vernal  equinox  in  the  month 
of  March.  It  continues  to 
move  north  until  June  21, 
when  it  reaches  its  greatest 
northern  declination  (23°  27'). 
For  several  days  at  this  time 
the  Sun  moves  very  little  in 
declination  and  seems  (so  far 
as  its  motion  in  declination  is 
concerned)  to  stand  still.  For 
this  reason  the  ancients  called 
the  Sun's  place  about  June 
21  the  summer  solstice  (Latin 
sol  =  the  Sun,  sistere  =  to 
cause  to  stand  still).  Its  right- 
ascension  is  VI  hours. 


APPARENT  MOTION  OF  THE  SUN.  163 

From  June  21  to  September  22  the  Sun  remains  north 
of  the  equator,  but  its  declination  grows  less  and  less 
during  these  months.  Finally  on  September  23  the  Sun 
crosses  the  equator  once  more  going  southwards  at  a  point 
called  the  autumnal  equinox.  Its  declination  is  then  zero 
(because  it  is  on  the  equator)  and  its  right-ascension  is  XII 
hours  (because  it  is  180°  distant  from  the  vernal  equinox, 


FIG.  101. — THE  CELESTIAL  SPHERE  WITH  THE  EQUATOR  (AB) 
AND  THE  ECLIPTIC  (CD). 

P  is  the  north  pole  of  the  celestial  equator  ;  Q  is  the  north  pole  of  the 
Sun's  apparent  path,  the  ecliptic. 

the  zero  of  right-ascensions).  After  September  22  and 
until  the  succeeding  March  the  Sun  is  in  the  southern  half 
of  the  celestial  sphere.  Its  south  declination  continually 
increases  until  December  22,  when  it  is  23°  South,  in  right- 
ascension  XVIII  hours.  This  point  is  the  winter  solstice. 
From  the  winter  solstice  to  the  vernal  equinox  the  Sun  is 
moving  northwards  (in  declination)  and  always  eastwards 
(in  right-ascension)  along  the  ecliptic.  Finally  in  the 
succeeding  March  the  Sun  again  crosses  the  equator  at  the 
vernal  equinox  (R.A.  =  Oh,  Decl.  =  0°).  The  point  D  of 


164  ASTRONOMY. 

the  last  figure  is  the  summer  solstice ;  the  point  C  is  the 
winter  solstice. 

The  ecliptic,  as  well  as  the  equator,  is  marked  on  all 
globes;  and  the  annual  motion  of  the  Sun  can  be  illus- 
trated by  tracing  out  the  Sun's  path  day  hy  day.  It 
requires  about  365  days  for  the  Sun  to  move  around  the 
360°  of  the  ecliptic.  Hence  the  Sun  moves  eastward 


FIG.  102. — THE   CELEBTIAL  SPHERE. 
EF  is  the  celestial  equator,  IJ  the  ecliptic. 

among  the  stars  about  1°  per  day.  The  Sun's  angular 
diameter  is  about  half  a  degree.  Therefore  the  Sun  moves 
each  day  about  two  of  its  own  diameters. 

The  celestial  latitude  of  a  star  is  its  angular  distance  north  or  south 
of  the  ecliptic.  The  celestial  longitude  of  a  star  is  its  angular  dis- 
tance from  the  vernal  equinox,  measured  on  the  ecliptic  eastwards 
from  the  equinox.  The  degrees  of  celestial  longitude  for  half  the. 
year  a.re  marked  on  Fig.  1QO, 


LENGTH  OF  TEE  DAY  AT  DIFFERENT  SEASONS.    165 

The  sidereal  year  was  defined  (page  158)  as  the  interval 
of  time  between  two  successive  returns  of  the  Sun  to  the 
same  star.  Its  length  is  365  days,  6  hours,  9  minutes, 
9.3  seconds. 

The  astronomical  year  (the  year  as  commonly  used)  is 
the  interval  between  two  successive  returns  of  the  Sun  to 
the  same  equinox.  Its  length  is  365  days,  5  hours,  48 
minutes,  46  seconds.  It  is  shorter  than  the  sidereal  year 


FIG.    103. — THE    CELESTIAL    SPHERE    AS    IT    APPEARS    TO    AN 
OBSERVER  IN  84°  NORTH  LATITUDE  (PON  =  34°). 

The  ecliptic  is  not  drawn  on  this  figure. 

because  the  equinoctial  points  are  not  fixed  (as  the  stars 
are)  but  move  slowly.  This  will  be  explained  more  fully 
later  on. 

Length  of  the  Day  at  Different  Seasons  of  the  Year. — 
The  length  of  time  that  any  star  is  above  the  horizon  of 
an  observer  depends  first  on  the  observer's  latitude,  and 


166  ASTRONOMY. 

second  on  the  star's  declination.  We  have  just  seen  that 
the  Sun's  declination  is  about  23°  south  on  January  1,  5° 
north  on  April  1,  23°  north  on  July  1,  3°  south  on 
October  1. 

To  every  observer  the  Sun  will  be  above  the  horizon  for 
different  periods  at  different  times  of  the  year.  The 
summer  days  will  be  the  longest  and  the  winter  days  the 
shortest. 

Figure  103  represents  the  celestial  sphere  to  an  observer 
in  34°  north  latitude.  On  January  1  the  Sun  (Decl.  = 
south  23°)  will  cross  his  meridian  23°  south  of  the  point  (7 
(nearly  half  way  from  C  to  $),  and  will  describe  a  diurnal 
orbit  parallel  to  CWD  (the  equator).  It  will  remain  above 
the  horizon  a  short  time.  The  night  will  be  longer  than 
the  daylight  hours.  On  March  20  the  Sun  will  be  at  V 
(the  vernal  equinox).  It  will  cross  the  meridian  at  C  and 
will  remain  above  the  horizon  (NS)  twelve  hours.  The 
days  and  nights  will  be  equal.  On  July  1  the  Sun  is  in 
declination  23°  north  and  will  cross  the  meridian  11°  south 
of  Z  (CZ^  34°;  34°  -  23°  =  11°).  The  daylight  hours 
will  be  long. 

By  constructing  sucli  a  diagram  for  his  own  latitude  and  by  mark- 
ing the  place  of  the  sun  for  different  days  of  the  year  the  student 
can  say,  beforehand,  just  what  the  apparent  diurnal  path  of  the  sun 
will  be  for  any  day  in  any  year.  A  celestial  globe  set  for  his  latitude 
will  show  the  same  things.  He  should  notice  that  the  sun  rises  north 
of  his  east  point  in  the  summer  ;  in  the  east  point  at  the  equinoxes  ; 
south  of  the  east  point  in  the  winter.  The  sun's  diurnal  path  at  the 
equinoxes  of  Marchand September  isthe  celestial  equator,  at  the  winter 
solstice  it  is  the  tropic  of  Capricorn  ;  at  the  summer  solstice  it  is  the 
tropic  of  Cancer.  These  tropics  are  circles  of  the  celestial  sphere 
drawn  parallel  to  the  equator,  one  (Cancer]  23£°  north  of  it,  the  other 
(Capricorn)  23^°  south  of  it.  They  are  called  tropics  because  the  Sun 
there  turns  from  going  north  (or  south)  in  declination  and  begins  to 
go  south  (or  north).  They  are  marked  on  all  globes.  The  regions 
of  the  earth  between  the  latitudes  23^°  north  and  south  are  called  the 
tropics. 


LENGTH  OF  THE  DA  Y  AT  DIFFERENT  SEASONS. 


167 


If  the  observer  is  on  the  equator  of  the  Earth,  all  the 
aays  and  nights  of  the  whole  year  will  be  equal,  no  matter 
what  the  Sun's  declination  may  be.  (See  Fig.  105.) 


SOUTH  POLE 

FIG.  104.— THE  CIRCLES  OF  THE  EARTH. 


FIG.  105.— THE  CELESTIAL  SPHERE  AS  IT  APPEARS  TO  AN 
OBSERVER  ON  THE  EARTH'S  EQUATOR. 

All  the  stars  (and  the  Sun)  are  always  above  the  horizon  12  hours  and 
below  it  12  hours.    The  days  and  nights  are  all  equal. 


168 


ASTRONOMY. 


The  following  little  table  will  be  found  useful  and  interesting. 

THE  APPROXIMATE  TIME  OF  SUNRISE  FOR  OBSERVERS  BETWEEN 
30°  AND  48°  OF  NORTH  LATITUDE. 

N.  B.— The  column  of  the  table  headed  with  the  observer's  latitude  is 
the  one  to  be  consulted. 

N.  B  —The  approximate  time  of  sunset  is  as  many  hours  after  noon  as 
the  time  of  sunrise  is  before  it.  For  instance  on  May  1  in  latitude  44°  the 
sun  rises  at  4h  51m  A.M.  i.e.  7h  9m  before  noon.  The  approximate  time  of 
sunset  on  that  day  is  therefore  7h  9m  P.M. 


Latitude. 

30° 

32° 

34° 

36° 

38° 

40° 

42° 

44° 

46° 

48° 

Date. 

h.  m. 

h.  m. 

h.  m. 

h.  m. 

h.  m. 

h.  m. 

h.  m. 

h.  m. 

h.  m. 

h.  m. 

Jan.   1.  
11  
21  

6  56 
6  57 
6  56 

7  0 
7  1 
7  0 

7  5 
7  5 
7  3 

7  10. 
7  10 

7  7 

7  16 
7  16 
7  12 

7  22 
7  21 
7  18 

729 

7  27 
7  23 

7  36 
7  33 
7  28 

743 

7  40 
7  34 

7  51 

7  47 
7  41 

Feb.    1  
11  
21  

6  50 
6  41 
6  34 

6  54 
6  47 
6  36 

6  57 
6  50 
6  39 

7  1 
6  52 
6  41 

7  5 
6  55 
6  44 

7  9 
6  58 
6  46 

7  13 
7  1 
6  49 

7  18 
7  5 
6  51 

7  23 
7  9 
6  53 

7  28 
7  14 
6  57 

Mar.   1  
11  
21  

6  27 
6  14 
6  2 

6  28 
6  15 
6  2 

6  29 
6  16 
6  1 

6  31 
6  16 
6  1 

6  33 

6  17 
6  1 

6  34 

6  17 
6  1 

6  36 
6  18 
6  1 

6  38 
6  19 
6  0 

6  40 
6  20 
6  0 

6  42 
6  21 
6  0 

Apr.    1... 
11  

21  

5  49 

5  37 
5  27 

5  48 
5  35 
5  24 

5  47 
5  34 
5  22 

5  46 

5  as 

5  20 

5  45 
5  31 
5  17 

5  44 
5  29 

5  14 

543 

5  26 
5  11 

5  42 
5  24 

5  8 

5  41 
5  22 
5  4 

5  39 
5  19 
5  0 

May    1  
11  

21  

5  17 
5  9 
5  3 

5  14 
5  5 
4  58 

5  11 
5  1 
4  58 

5  7 
4  57 
4  49 

5  3 
4  52 
4  44 

5  0 
4  48 
4  39 

56 
43 
33 

4  51 
4  38 
4  27 

4  46 
4  33 
4  20 

4  41 
4  27 
4  13 

June   1.. 
11  
21  

4  58 
4  58 
4  59 

4  53 
4  52 
4  54 

4  48 

4  47 
4  48 

4  43 
4  41 
4  42 

4  38 
4  35 
4  36 

4  32 
4  30 
4  30 

25 
23 
23 

4  18 
4  15 
4  15 

4  11 
4  8 
4  8 

4  3 
3  59 
3  58 

July   1  
11  
21  

5  2 
5  6 
5  12 

4  56 
5  2 

5  7 

4  51 
4  57 
5  2 

4  45 
4  51 

4  58 

4  39 
4  45 
4  53 

4  34 
4  40 
4  48 

4  27 
4  34 
4  42 

4  19 
4  27 
4  36 

4  12 
4  19 
4  29 

4  4 
4  11 
4  22 

Aug-  iJ.:.:.. 

21  

5  18 
5  24 
5  30 

5  14 

5  21 
5  28 

5  10 
5  17 
5  25 

5  6 
5  14 
5  23 

5  2 
5  10 
5  20 

4  57 

5  7 
5  17 

4  52 
5  2 
5  13 

4  47 
4  57 
5  10 

4  42 

4  53 
5  6 

4  35 

4  47 
5  2 

Sept.   1... 
11  
21  

5  36 
5  42 
5  47 

5  34 

5  41 
5  47 

5  32 
5  40 
5  47 

5  31 
5  39 
5  47 

5  29 
5  38 
5  46 

5  27 
5  37 
5  46 

5  25 
5  35 
5  45 

5  23 
5  34 
5  45 

5  21 
5  33 
5  45 

5  18 
5  31 
5  44 

Oct.    1... 
11  
21  

5  54 
6  0 
6  6 

5  54 
6  1 
6  9 

5  55 
6  2 
6  11 

5  55 
6  3 
6  13 

5  56 
6  5 
6  16 

5  57 

6  7 
6  18 

5  58 
6  8 
6  21 

5  59 
6  10 
6  23 

5  59 
6  12 
6  25 

6  0 
6  14 
6  28 

Nov.    1  . 
11  
21  

6  14 
6  22 
6  30 

6  17 
6  25 
6  34 

6  21 
6  29 
6  38 

6  24 
6  33 
6  42 

6  26 

6  37 
6  47 

6  29 
6  41 
6  52 

6  33 
6  45 
6  57 

6  37 

6  50 
7  3 

6  41 
6  55 

7  10 

645 

7  1 
7  17 

Dec.   1.. 

11  
21  

6  38 
6  46 
6  53 

6  43 
6  51 
6  58 

6  47 
6  56 
7  3 

6  52 
7  1 

7  8 

6  57 
7  7 
7  13 

7  2 
7  12 
7  19 

7  8 
7  18 
7  26 

7  15 
7  25 
7  33 

7  22 
7  33 
7  40 

7  29 
7  41 
7  48 

THE  ZODIAC.  169 

If  the  observer  is  at  the  Earth's  north  pole  the  Sun 
would  be  continuously  above  his  horizon  so  long  as  the  Sun 
was  in  the  northern  half  of  the  celestial  sphere,  that  is, 
from  March  to  September;  and  continuously  below  his 
horizon  from  September  to  March.  An  observer  at  the 
south  pole  of  the  Earth  has  daylight  continuously  from 
September  to  March  and  continuous  darkness  from  March 
to  September. 


FIG.  106.— THE  CELESTIAL  SPHERE  AS  IT  WOULD  APPEAR  TO  AN 
OBSERVER  AT  THE  NORTH  POLE  OP  THE  EARTH. 

The  Sun  would  be  above  the  horizon  all  the  time  from  March  20  to  Sep- 
tember 22.  The  day  would  be  six  months  long.  The  sun  would  be  below 
the  horizon  all  the  time  from  September  22  to  March  20.  The  night  would 
also  be  six  months  long. 

The  Zodiac  and  the  Signs  of  the  Zodiac. — The  zodiac  is 
a  belt  in  the  heavens,  extending  some  8°  on  each  side  of 
the  ecliptic,  and  therefore  about  16°  wide  (see  figure  50). 
The  planets  known  to  the  ancients  are  always  seen  within 
this  belt.  At  a  very  early  day  the  zodiac  was  mapped  out 
into  twelve  regions  known  as  the  signs  of  the  zodiac,  the 
names  of  which  have  been  handed  down  to  the  present 
time.  Each  of  these  regions  was  supposed  to  be  the  seat 
of  a  constellation  or  group  of  stars.  Commencing  at  the 


170  ASTRONOMY. 

vernal  equinox,  the  first  thirty  degrees  of  the  ecliptic 
through  which  the  Sun  passed,  or  the  region  among  the 
stars  in  which  it  was  found  during  the  month  following, 
was  called  the  sign  Aries.  The  next  thirty  degrees  was 
called  the  sign  Taurus,  and  so  on.  The  names  of  the  signs 
in  order  are  : 

Spri        (    1.  «f  Aries.    The  sun  enters  the  sign  Aries,  March  20. 

sins      )    2-  »  Tauras-          "        "          "         Taurus,  April  20. 

'     (    3.  n  Gemini.          "       "          "         Gemini,  May  20. 
e  ,«      ^(    4-  ®  Cancer.  "        "          "        Cancer,  June  21. 

ZT      5-*Leo-  "       "          "        Leo.Mj^. 

(    6.  iTE.  Virgo.  Virgo,  August  22. 

Autumn  (    7"  -  Libra"             "  "  "  Libra>  September  22. 

•<    8.  TTI,  Scorpius.  Scorpius,  October  23. 

(    9.   #  Sagittarius.    "  "  "  Sagittarius,  Nov.  23. 

yr.          r  10.  V3  Capricornus.  "  "  "  Capricornus,  Dec.  21. 

•<  11.  ^Aquarius.       "  "  "  Aquarius,  Jan.  20. 

SlgnS'     (  12.  K  Pisces.            "  "  "  Pisces,  February  19. 


Each  of  the  signs  of  the  zodiac  coincides  roughly  with  a  con- 
stellation in  the  heavens  ;  and  thus  there  are  twelve  constellations 
called  by  the  names  of  these  signs,  but  the  signs  and  the  constella- 
tions no  longer  accurately  correspond  as  they  formerly  did.  Although 
the  Sun  now  crosses  the  equator  and  enters  the  sign  Aries  on  the  20th 
of  March,  he  does  not  reach  the  constellation  Aries  until  nearly  a 
month  later.  This  arises  from  the  precession  of  the  equinoxes,  to  be 
explained  hereafter. 

—  Why  are  the  stars  fixed?  Are  the  p]&nets  fixed?  Which  way 
does  the  sun  move  among  the  stars—  eastwards  or  westwards?  How 
long  does  it  take  the  sun  to  make  a  complete  circuit  of  the  heavens  ? 
What  is  the  reason  that  the  sun  appears  to  move  among  the  stars  ? 
What  is  the  earth's  radius-vector?  What  is  the  plane  of  the  ecliptic  ? 
What  is  a  sidereal  year?  Describe  the  way  in  which  our  notions  of 
the  directions  east  and  west  have  arisen.  The  stars  in  their  diurnal 
orbits  rise  in  the  -  The  earth  turns  on  its  axis  from  -  to  - 
The  sun  moves  from  -  to  -  among  the  stars.  The  earth  moves 
in  its  real  orbit  in  the  same  direction  that  the  sun  moves  in  its  ap- 
parent path,  from  -  to  -  therefore.  What  is  the  geocentric  or  the 
heliocentric  place  of  a  body?  What  is  the  vernal  equinox?  the 
autumnal  equinox  ?  the  winter  solstice  ?  the  summer  solstice  ?  Why 
are  these  points  called  solstices?  How  long  is  the  sun  in  the 


OBLIQUITY  OF  THE  ECLIPTIC. 


171 


northern  half  of  the  celestial  sphere  ?  About  how  far  does  the  sun 
move  in  the  sky  each  day  ?  What  is  an  astronomical  year  ?  Why 
are  our  winter  days  shorter  than  our  days  in  summer  ?  How  long 
is  a  summer  day  to  an  observer  at  the  earth's  north  pole  ?  How  long 
is  a  day  to  an  observer  at  the  earth's  equator  ?  What  is  the  Zodiac  ? 
What  are  the  signs  of  the  Zodiac  ? 

22.  Obliquity  of  the  Ecliptic. — The  obliquity  of  the 
ecliptic  is  the  angle  between  the  plane  of  the  ecliptic  and 
the  plane  of  the  celestial  equator.  It  is  the  angle  between 
the  planes  DOC  and  AOB  in  the  figure.  It  is  measured 


FIG.  107. — OBLIQUITY  OP  THE  ECLIPTIC. 
A  B  is  the  celestial  equator,  CD  is  the  ecliptic. 

by  the  arc  DB  or  A  G.  DB  is  the  Sun's  greatest  northern 
declination;  A C is  the  Sun's  greatest  southern  declination. 
As  soon  as  we  have  measured  either  of  these  (with  a 
meridian-circle,  for  example)  the  obliquity  is  known.  It  is 
about  23^°.  It  was  determined  by  the  ancient  astronomers 
quite  accurately  by  observing  the  shadow  of  an  obelisk  at 
the  times  of  the  summer  and  winter  solstices.  At  the 
summer  solstice  the  Sun  has  its  greatest  north  declination, 
and  therefore  its  meridian  altitude  on  that  day  is  a  maxi- 


172 


ASTRONOMY. 


mum.     Its  meridian  altitude  on  the  day  of  the  winter 
solstice  is  a  minimum. 

If  AB  is  an  obelisk  and  the  line  Ed  is  a  north  and  south 
line,  and  if  the  Sun  is  on  the  line  Ad  on  December  22  and 
on  Aj  on  June  21,  then  the  shadow  of  the  obelisk  will  be 
Bj  in  June  (the  shortest  shadow  of  the  year)  and  Bd  in 
December  (the  longest  meridian  shadow  of  the  year)  and 
Bm  at  the  equinoxes.  The  angle  dAj  can  be  measured. 
It  is  equal  to  twice  the  obliquity  and  mAB  measures  the 


Zenith 


m  j 

FIG.  108. — THE  OBLIQUITY  OF  THE  ECLIPTIC — 
determined  by  the  shadow  of  an  obelisk  at  a  place  whose  latitude  is  45*  N. 

latitude  of  the  place,  as  the  student  can  readily  prove  for 
himself. 

The  Cause  of  the  Seasons  on  the  Earth. — In  each  and 
every  year  we,  who  live  in  the  temperate  zones  of  the 
Earth,  witness  the  coming  of  spring,  of  summer,  of 
autumn,  of  winter.  They  come  and  go  in  a  cycle  of  a 
year,  and  the  cause  of  the  change  of  seasons  must  therefore 
depend  on  the  Earth's  annual  revolution  in  its  orbit.  The 


THE  SEASONS.  173 

different  seasons  are  marked  by  changes  in  the  quantity  of 
heat  received  from  the  Sun.  In  the  summer  the  altitude 
of  the  Sun  is  high  and  the  days  are  long.  In  the  winter 
the  altitude  of  the  Sun  is  not  so  high  and  the  days  are 
shorter.  The  difference  between  the  heat  of  summer  and 
winter  depends  chiefly  on  the  differences  named.  The 
Earth  revolves  about  the  Sun  in  an  orbit  which  is  very 
nearly  a  circle,  so  that  the  change  of  seasons  does  not 
depend  on  the  varying  distance  of  the  Earth  from  the  Sun. 
As  a  matter  of  fact  the  Earth  is  somewhat  nearer  to  the 
Sun  in  January  than  it  is  in  July. 


FIG.  109.— THE  ECLIPTIC,  CD,  AND  THE  CELESTIAL  EQUATOR, 

AB,  WITH   THEIR  POLES,   Q  AND   P. 

The  Sun's  apparent  motion  is  in  the  ecliptic  CD.  The 
vernal  equinox  is  at  E,  the  summer  solstice  at  />,  the 
autumnal  equinox  at  F,  the  winter  solstice  at  C.  The  arc 
BD  =  AC=  23|°,  the  obliquity  of  the  ecliptic. 

The  Sun's  North-polar  distance  at  E  is  90°; 
"       "  "  i(        <e  D  ((  66A°* 

a        (t  n  (t        a    TJI  tf  9()°. 

«       «  «  «        «   (J  « 


174  ASTRONOMY. 

In  Fig.  110  the  oval  line  represents  the  path  of  the  Earth 
in  its  annual  revolution  about  the  Sun  in  the  ecliptic.  The 
line  N8  in  each  picture  of  the  Earth  represents  the  Earth's 
axis,  ^its  north  end.  The  Earth's  axis  is  always  directed 
to  a  point  very  near  to  the  star  Polaris  at  all  times  of  the 
year,  that  is,  wherever  the  Earth  may  be  in  her  orbit. 
Hence  the  four  lines  NS  are  drawn  parallel  to  each  other. 


FIG.  110.—  THE  SEASONS. 

The  Earth  is  shown  in  four  positions  in  its  orbit.  A  =  the  winter  sol- 
stice ;  B  =  the  vernal  equinox  ;  C  =  the  summer  solstice  ;  D  =  the  au- 
tumnal equinox.  The  orbit  of  the  Earth  is  nearly  a  circle.  It  is  much 
foreshortened  in  the  picture. 

The  Earth's  axis  is  perpendicular  to  the  celestial  equator, 
but  it  is  inclined  to  the  ecliptic  by  an  angle  of  23^°,  and 
it  has  been  so  drawn. 

If  the  student  will  join  the  centre  of  the  Sun  (S)  with 
the  centre  of  the  Earth  in  each  one  of  the  four  positions 
drawn  he  will  see  that,  as  has  been  said, 

The  Sun's  N.P.D.  at  A  (winter  solstice)        is  HSf; 
"         "         "         "  B  (vernal  equinox)       is  90 
"         "         "         "  C  (summer  solstice)      is  66 
"         "         <<         "  D  (autumnal  equinox)  is  90 


° 


THE  SEASONS. 


175 


He  can  also  prove  that  the  Sun's  altitude  to  any  observer 
in  the  northern  hemisphere  is  greater  in  summer  than  in 
winter  by  drawing  the  horizon  of  an  observer  on  the  same 
parallel  of  the  Earth  at  A  and  at  G. 

The  Sun  shines  on  one  half  of  the  Earth  only — namely 
on  that  half  which  is  turned  toward  him.  This  hemi- 
sphere is  left  bright  in  each  of  the  figures  ABCD.  The 
other  half  of  the  sphere  is  dark.  Consider  the  picture  at 

N, 


FIG.  111. — A.  THE  EARTH  AT  THE  WINTER  SOLSTICE. 

A  (winter  solstice)  and  remember  that  the  Earth  is  turning 
on  its  axis  every  24  hours.  Every  observer  on  the  Earth, 
in  any  latitude,  is  carried  round  his  parallel  of  latitude  by 
the  Earth's  rotation  once  in  every  24  hours.  The  parallels 


FIG.  112.— B.  THE  EARTH  AT  THE  VERNAL  EQUINOX. 

of  latitude  are  drawn  in  the  picture.  A  person  near  N 
will  remain  in  darkness  during  the  whole  24  hours.  A 
person  anywhere  in  the  northern  hemisphere  of  the  Earth 


176 


ASTRONOMY. 


will  be  less  than  half  the  time  in  the  light,  more  than  half 
the  time  in  darkness.  The  Sun  will  be  less  than  half  the 
time  above  his  horizon.  The  daylight  hours  will  be  shorter 
than  the  hours  of  darkness.  This  is  the  time  of  winter  in 
the  northern  hemisphere  of  the  Earth. 

Take,  next,  the  Earth  at  the  vernal  equinox  B.     Half 

N, 


FIG.  113.— C.  THE  EARTH  AT  THE  SUMMER  SOLSTICE. 

of  the  Earth  is  lighted  by  the  Sun,  and  the  Sun's  rays  just 
reach  the  two  poles  iVand  S.  The  days  and  nights  are 
equal.  At  the  summer  solstice  C  an  observer  at  the 
Earth's  north  pole  has  perpetual  day;  and  the  Sun  is 
above  the  horizon  of  every  person  in  the  northern  hemi- 


FIG.  114.— D.  THE  EARTH  AT  THE  AUTUMNAL  EQUINOX. 

sphere  for  more  than  half  the  24  hours.  The  days  are 
longer  than  the  nights.  At  the  autumnal  equinox,  Z>,  the 
circumstances  are  like  those  at  the  vernal  equinox. 


THE  SEASON'S. 


m 


The  foregoing  explanation  of  Fig.  110  illustrates  the 
dependence  of  the  seasons  upon  the  length  of  time  that  the 
Sun  is  above  the  horizon.  The  altitude  of  the  Sun  above 
the  horizon  also  plays  an  important  part  in  producing  the 
change  of  the  seasons.  (See  Fig.  115). 

In  the  figure  a  beam  of 
sunshine  having  the  cross- 
section  ABCD  strikes  the 
soil  cbDA  at  an  angle  h.  It 
is  clear  that  the  area  cbDA 
is  greater  than  the  area 
ABCD.  The  amount  of 
heat  in  the  sunbeam  is 
always  the  same.  This  con-  FlG  115._THB  EFFECT  OF  THE 
stant  amount  of  heat  is  dis-  SUN'S  ELEVATION  ON  THE 
tributed  over  a  larger  surface  £0M?™T8°0FILHEAT  IMPARTED 
according  as  the  altitude  of 

the  Sun  is  less.  Hence  in  a  winter's  day,  when  the  Sun 
even  at  noon  is  low,  each  square  mile  of  soil  receives  less 
heat  than  it  receives  in  summer,  when  the  Sun  is  high. 


FIG.  116. — THE  MERIDIAN  ALTITUDE  OF  THE  SUN  AT  £  is 
EQUAL  TO  (90°  _  0  +  5) ;  HS  =  HQ  +  Q8. 

At  a  place  on  the  Earth  whose  latitude  is  45°  (=  0)  the 
meridian-altitude  of  the  Sun 


178  ASTRONOMY. 

is  45°    on  March  20  (90°  —  45°  -f  0°); 

"  68i°  i(  June  21  (90°  -  45°  +  23^°); 

"  45°     "  September  22  (90°  —  45°  -f  0°); 

"  2H°  "  December  22  (90°  —  45°  —  23£°). 
Therefore  the  Sun's  rays  are  inclined  to  the  soil  at  very 
different  angles  at  different  dates,  and  the  amount  of  heat 
received  per  square  mile  varies.  Not  only  is  less  heat  per 
square  mile  received  in  December  than  in  June,  but  it  is 
received  for  a  shorter  period.  In  latitude  45°  the  Sun  is 
above  the  horizon  for  about  15£  hours  on  June  21  (see  the 
table  on  page  168),  while  on  December  22  it  is  above  the 
horizon  for  a  little  more  than  8-J  hours.  There  are  two 
reasons,  then,  for  the  change  of  seasons:  first,  the  duration 
of  sunshine  is  longer  at  some  dates  than  at  others,  second 
the  amount  of  the  Sun's  heat  received  per  square  mile  per 
hour  is  greater  at  some  dates  than  at  others. 

—  The  student  should  take  a  pin  and  put  it  on  the  various  parallels 
of  latitude  in  the  four  diagrams  ABCD,  Fig.  110.  The  rotation  of 
the  Earth  carries  an  observer  round  his  own  parallel  of  latitude.  The 
pictures  show  whether  the  observer  is  more  or  less  than  1 2  hours  in 
the  light  of  the  Sun — whether  his  days  are  longer  or  shorter  than  his 
nights.  They  also  show  how  the  altitude  of  the  Sun  varies  at  dif- 
ferent seasons  of  the  year.  Notice  that  an  observer  on  the  Earth's 
equator  always  has  days  and  nights  of  equal  length,  no  matter  what 
the  season  of  the  year.  Prove  that  the  Sun  is  always  in  the  zenith 
to  some  observer  in  the  Earth's  torrid  zone. 

What  is  the  obliquity  of  the  ecliptic?  How  many  degrees  is  it? 
Show  how  it  can  be  determined  by  observing  the  lengths  of  the 
shadow  of  an  obelisk.  What  are  the  two  causes  of  the  change  of 
seasons  on  the  Earth  ? 


CHAPTER  IX. 

THE  APPARENT  AND  REAL  MOTIONS  OF  THE  PLANETS 
-KEPLER'S  LAWS. 

23.  The  Apparent  Motions  of  the  Planets  to  an  Observer 
on  the  Earth— Their  Real  Motions  in  Their  Orbits.— The 
apparent  motions  of  the  planets  were  studied  by  the  ancients 
by  mapping  down  their  positions  among  the  fixed  stars  from 
night  to  night.  The  same  process  can  be  followed  to-day 
by  any  one  who  will  give  the  time  to  it.  The  place  of  the 
planet  must  be  fixed  by  observation  each  night,  with  refer- 
ence to  stars  near  it,  and  then  this  place  must  be  trans- 
ferred to  a  star-map,  like  those  printed  at  the  end  of 
this  book,  for  instance.  A  curved  line  joining  the  different 
apparent  positions  of  the  planet  on  different  nights  will 
represent  its  apparent  path. 

Astronomers,  who  are  provided  with  accurate  instru- 
ments such  as  meridian-circles,  fix  the  positions  of  the 
planets  by  determining  their  right-ascensions  and  declina- 
tions every  night.  By  platting  these  positions  on  a  map 
they  obtain  a  representation  of  the  apparent  orbit  with 
great  accuracy. 

Something  of  the  same  sort  can  be  done  by  the  student  with  much 
simpler  instruments.  He  needs  only  a  common  watch  and  a  straight 
ruler  some  three  feet  long,  together  with  a  star-map.  Suppose  that  he 
wishes  to  determine  the  place  of  the  planet  Mars  (  $  ).  The  first  step 
is  to  identify  the  planet  in  the  sky,  by  its  brightness,  its  place,  or  by 
its  motion.  He  then  selects  two  bright  stars  not  very  far  away  from 
it  (let  us  call  them  A  and  B  for  convenience). 

Holding  up  the  ruler  so  that  its  edge  passes  through  the  two 
stars,  he  notices  that  it  passes  very  nearly  through  the  planet,  which 

179 


FIG.  117. — COPERNICUS. 
Born  1473,  died  1543. 


180 


APPARENT  MOTIONS  OF  THE  PLANETS.        181 

is,  however,  let  us  say,  a  little  to  the  west  of  the  line.  On  the  star- 
map  he  must  find  the  two  stars  A  and  B.  Suppose  that  they  are 
a  and  ft  Auriga,  (between  the  numbers  105°  and  120°  at  the  top  of 
Plate  II).  A  dot  must  now  be  put  on  the  map  in  the  proper  position 


East 


to  represent  the  place  of  the  planet ;  and  the  dot  must  be  numbered 
(1).  In  his  note-book  opposite  1  the  observer  must  write  the  year, 
the  month,  the  day,  and  the  hour  of  observation  thus  : 

1.  1899,  February  27,  9h  P.M. 

The  place  of  the  planet  is  much  more  accurately  fixed  if  the 
observer  makes  allineations  with  four  stars,  thus  : 

C  might  be  d  AurigcB  on  Plate  II  and  D  a  star  given  but  unnamed 
there. 

On  succeeding  nights  other  positions  of  the  planet  can  be  obtained 
in  the  same  way,  and  its  apparent  path  can  be  had  by  joining  the 
different  positions.  The  times  of  each  observation  are  to  be  noted. 
The  positions  of  other  planets  as  Mercury,  Venus,  Jupiter,  and 
Saturn  can  also  be  studied  from  night  to  night,  and  their  apparent 
paths  fixed  in  like  manner.  Observations  of  this  kind,  if  continued 
long  enough,  will  give  the  apparent  paths  of  the  different  planets  in 
the  sky.  The  courses  of  the  Sun  and  Moon  can  be  studied  in  the 
same  manner,  except  that  observations  of  the  Sun  must  be  made  near 
the  times  of  sunset  and  sunrise,  because  it  is  only  at  these  times  that 
stars  are  visible  near  it. 

If  snch  observations  are  made  the  student  can  discover 
for  himself  what  the  ancients  knew  very  well,  namely,  that 


182  ASTRONOMY. 

there  are  heavenly  bodies  with  apparent  motions  of  three 
very  different  kinds.  The  Sun  and  Moon  have  apparent 
motions  of  one  kind.  If  we  mark  down  the  positions  of 
the  San  day  by  day  upon  a  star-chart,  they  will  all  fall  into 
a  regular  circle  which  marks  out  the  ecliptic,  and  its  motion 
is  always  towards  the  east.  The  monthly  course  of  the 
Moon  is  found  to  be  of  the  same  nature;  and  although  its 
motion  is  by  no  means  uniform  in  a  month,  it  is  always 
towards  the  east,  and  always  along  or  very  near  a  certain 
great  circle. 

Venus  and  Mercury  have  motions  of  a  different  kind. 
The  apparent  motion  of  these  bodies  is  an  oscillating  one 
on  each  side  of  the  Sun.  If  we  watch  for  the  appearance 
of  one  of  these  planets  after  sunset  from  evening  to  even- 
ing, we  shall  by  and  by  see  it  appear  above  the  western 
horizon.  Night  after  night  it  will  be  farther  and  farther 
from  the  Sun  until  it  attains  a  certain  maximum  distance; 
then  it  will  appear  to  return  towards  the  Sun  again,  and  for 
a  while  it  will  be  lost  in  its  rays.  A  few  days  later  it  will 
reappear  to  the  west  of  the  Sun,  and  thereafter  be  visible 
in  the  eastern  horizon  before  sunrise.  In  the  case  of 
Mercury  the  time  required  for  one  complete  oscillation 
back  and  forth  is  about  four  months ;  and  in  the  case  of 
Venus  it  is  more  than  a  year  and  a  half. 

The  third  class  comprises  Mars,  Jupiter,  and  Saturn. 
The  general  or  average  motion  of  these  planets  is  towards 
the  east,  a  complete  revolution  around  the  celestial  sphere 
being  performed  in  two  years  in  the  case  of  Mars,  12  years 
in  the  case  of  Jupiter,  and  30  years  in  that  of  Saturn. 
But,  instead  of  moving  uniformly  forward,  they  seem  to 
have  a  swinging  motion ;  first,  they  move  forward  or  toward 
the  east  through  a  pretty  long  arc,  then  backward  or  west- 
ward through  a  short  one,  then  forward  through  a  longer 
one,  etc.  It  is  by  the  excess  of  the  longer  arcs  over  the 
shorter  ones  that  the  circuit  of  the  heavens  is  made. 


APPARENT  MOTIONS  OF  THE  PLANETS        183 

Observations  of  the  planets  will  show  that  each  one  of  them 
has  an  apparent  motion  like  those  just  described.  The 
problem  is  to  discover  the  real  cause  of  these  observed 
motions. 

The  general   motion  of  the   San,   Moon,  and  planets 
among  the  stars  being  towards  the  east,  observed  motions 


FIG.  120. 

If  S  is  the  Sun,  E  the  Earth,  CLM  the  orbit  of  an  inferior  planet,  then 
the  planet  is  in  inferior  conjunction  at  7,  at  superior  conjunction  at  C,  at 
its  greatest  elongation  from  the  Sun  at  L  and  M. 

in  this  direction  are  called  direct;  motions  towards  the  west 
are  called  retrograde.  During  the  periods  between  direct 
and  retrograde  motion  the  planets  will  for  a  short  time 
appear  stationary. 

The  planets  Venus  and  Mercury  are  said  to  be  at  greatest 
elongation  when  at  their  greatest  angular  distance  from  the 
Sun. 

An  inferior  planet  is  said  to  be  in  conjunction  with  the 
Sun  when  both  planet  and  Sun  are  in  the  same  direction 
as  seen  from  the  Earth.  It  is  in  inferior  conjunction  when 
it  is  between  the  Sun  and  Earth;  in  superior  conjunction 
when  the  Sun  is  between  the  Earth  and  the  planet.  A 
superior  planet  is  said  to  be  in  opposition  to  the  Sun  when 


184  ASTRONOMY. 

the  planet  is  directly  opposite  in  direction  to  the  San  as 
seen  from  the  Earth. 

Arrangements  and  Motions  of  the  Planets  of  the  Solar 
System. — The  Sun  is  the  centre  of  the  solar  system  and  all 


FIG.  121. — THE  ORBITS  OF  MERCURY,  VENUS,  THE  EARTH,  MARS, 
AND  JUPITER. 

The  distance  from  the  Sun  to  the  Earth  is  93,000,000  miles  ;  from  the  Sun 
to  Jupiter  is  481,000,000  miles  ;  the  other  distances  are  in  proportion. 

the  planets  revolve  about  the  San.  Some  of  the  planets 
have  satellites  or  moons  that  revolve  about  the  planet  while 
the  planet  itself  revolves  about  the  Sun.  Our  own  Moon 
is  such  a  satellite.  The  orbits  of  the  planets  are  all  nearly, 
but  not  exactly,  in  the  same  plane,  namely,  in  the  plane  of 
the  Earth's  orbit — the  ecliptic. 


ORBITS  OF  TEE  PLANETS. 


185 


S 

J 

Stj 

NAME. 

1 

|| 

Sidereal  Period  of  Revolution. 

co 

-S  ^3 

.22  ^ 

Q 

Group  of    (  Mercury 
Planets  each      Venus  .  . 

9 

0.39 
0.72 

88  days  =    3    months  J_  . 
225     "     =    7£ 

about  the    •{   EV,™/;, 
size  of  the     }  ^rm  '  ' 
Earth.        L  Mars  .  .  . 

e 

6 

1.00 
1.52 

3654  "     =  12 
687     "     =  22£ 

The  Small  Planets... 

•  • 

About 
2.65 

3  to  8  years. 

(  Jupiter.  . 

2| 

5.20 

11  &  years. 

Groups  of      Saturn.  . 

*> 

9.54 

29i       " 

ISIS?8       g~»«- 

(^  Neptune 

6 
J 

19.18 
30.05 

84 
164  A     " 

*  The  distance  of  the  Earth  =  1.00  =  93,000,000  miles. 

The  planets  Mercury  and  Venus  which,  as  seen  from  the 
earth,  never  appear  to  recede  very  far  from  the  Sun,  are  in 
reality  those  which  revolve  inside  the  orbit  of  the  Earth. 
The  planets  Mars,  Jupiter,  and  Saturn  are  more  distant 
from  the  San  than  the  Earth  is.  Uranus  and  Neptune 
are  planets  generally  invisible  except  in  the  telescope,  and 
their  orbits  are  outside  of  that  of  Saturn.  On  the  scale 
of  Fig.  121  the  orbit  of  Neptune,  the  outermost  planet, 
would  be  more  than  thirty  inches  in  diameter. 

Inferior  planets  are  those  whose  orbits  lie  inside  that  of 
the  Earth,  as  Mercury  and  Venus. 

Superior  planets  are  those  whose  orbits  lie  outside  that 
of  the  Earth,  as  Mars,  Jupiter,  Saturn,  etc.  The  ancient 
astronomers  gave  these  names  and  they  have  been  retained 
in  use,  although  they  now  have  little  significance. 

The  farther  a  planet  is  situated  from  the  Sun  the  slower 
is  its  motion  in  its  orbit.  Therefore,  as  we  go  outwards 
from  the  Sun,  the  periods  of  revolution  are  longer,  for  the 


186  ASTRONOMY. 

double  reason  that  the  planet  has  a  larger  orbit  to  describe 
and  moves  more  slowly  in  its  orbit.  The  Earth  moves  18£ 
miles  per  second  in  its  orbit,  while  Saturn  moves  but 
6  miles  per  second. 

An  observer  on  the  Sun  at  S  would  see  the  Earth  along 
the  lines  $1,  S%,  $3,  etc.  If  these  lines  are  prolonged 
(to  the  right  hand  in  the  figure)  the  Earth  would  seem,  to 
an  observer  on  the  Sun,  to  move  eastwardly  among  the 


FIG.  122. — THE  MOTION  OF  THE  EARTH  IN  ITS  ORBIT — IT  is 
DIRECT  MOTION. 

stars  (see  page  158).  The  real  motion  of  the  Earth  seen 
from  the  Sun  is  direct.  We  have  proved  on  page  159  that 
the  apparent  motion  of  the  Sun  is  always  direct  also.  The 
plane  of  the  Earth's  orbit — the  ecliptic — is  the  plane  in 


MOTIONS  OF  THE  PLANETS.  187 

which  all  the  other  planets  revolve  very  nearly.  It  is  to 
the  slower  motion  of  the  outer  planets  that  the  occasional 
apparent  retrograde  motion  of  the  planets  is  due,  as  may 
be  seen  by  studying  Fig.  123.  The  apparent  position  of 
a  planet,  as  seen  from  the  Earth,  is  determined  by  the 
line  joining  the  Earth  and  planet.  We  see  the  planet 
along  this  line.  Supposing  this  line  to  be  continued  so  as 


FIG.  123. 

The  apparent  motion  of  a  superior  planet,  as  seen  from  the  Earth,  is 
sometimes  direct  and  sometimes  retrograde.  The  motion  is  always  retro- 
grade when  the  planet  is  nearest  the  Earth,  always  direct  when  the 
planet  is  farthest  from  the  Earth. 

to  intersect  the  celestial  sphere,  the  apparent  motion  of  the 
planet  will  be  defined  by  the  motion  of  the  point  in  which 
the  line  meets  the  celestial  sphere.  If  this  motion  is 
towards  the  east  the  motion  of  the  planet  is  direct;  if  this 
motion  is  towards  the  west,  the  motion  of  the  planet  is 
retrograde. 

Let  us  consider  the  case  of  one  of  the  superior  planets.  Its  orbit 
is  outside  of  the  Earth's  orbit.  Its  motion  in  its  orbit  is  slower  than 


188  ASTRONOMY. 

the  Earth's  motion  in  its  orbit.  Let  S  be  the  Sun,  ABCDEF  the 
orbit  of  the  Earth  and  EIKLMN  the  orbit  of  a  superior  planet — 
Mars,  for  example.  The  real  motion  of  Mars  is  direct.  It  moves 
round  its  orbit  in  the  direction  of  the  arrow,  just  as  the  Earth  moves 
round  its  orbit  in  the  direction  marked.  In  both  cases  the  real  mo- 
tion is  from  west  to  east. 

When  the  Earth  is  at  A,  Mars  is  at  H 
"       "       "        "    B,      "       "     I 

"       "       ••       "     C,       "       ••    K 
"       "       "       "    D,      "       "    L 

"    E,       "       "    M 
„       „       ,<       „    Ff       „       „    N 

As  the  Earth  moves  faster  than  Mars  the  arcs  AB,  BC,  CD,  DE, 
EF  correspond  to  greater  angles  at  8  than  do  the  arcs  HI,  IK,  KL, 
LM,  MN. 

When  the  Earth  is  at  A  and  Mars  at  H,  an  observer  on  the  Earth 
will  see  Mars  along  the  line  AH.  This  line  meets  the  celestial 
sphere  at  0.  Mars  will  then  appear  to  be  projected  among  the  stars 
near  0.  When  the  Earth  is  at  B  and  Mars  at  /,  the  planet  will  be 
viewed  along  the  line  BP  and  it  will  be  seen  on  the  celestial  sphere 
among  the  stars  near  P.  While  the  Earth  is  moving  in  its  orbit 
from  A  to  B  Mars  will  appear  to  move  (eastwards)  among  the  stars 
from  0  to  P.  Its  apparent  motion  is  in  the  same  direction  as  the 
Earth's  real  motion.  When  the  Earth  is  at  C  and  Mars  at  K  the 
planet  will  be  seen  along  the  line  (/^(prolonged).  Its  apparent  place 
among  the  stars  will  be  slightly  to  the  west  of  P — it  will  appear  to 
have  moved  backwards — its  apparent  motion  is,  at  this  time,  retro- 
grade. 

When  the  Earth  is  at  C  Mars  is  in  opposition  to  the  Sun.  The 
Sun  and  Mars  are  seen  from  the  Earth  in  opposite  directions.  The 
apparent  motion  of  ail  superior  planets  at  the  time  of  opposition  is 
retrograde. 

While  the  Earth  is  moving  from  G  to  D  in  its  orbit,  Mars  is  mov- 
ing from  Kto  L  in  its  orbit,  and  the  apparent  position  of  Mars  on 
the  celestial  sphere  is  moving  to  the  west — in  a  retrograde  direction. 
As  the  Earth  moves  from  D  to  E  Mars  moves  from  L  to  M  and  the 
planet  is  seen  along  the  lines  DL  and  EM  prolonged.  These  lines 
are  parallel.  They  meet  the  celestial  sphere  in  the  same  group  of 
stars.  The  planet,  therefore,  seems  to  stay  in  the  same  position 
among  the  stars.  It  appears  to  be  stationary  just  after  opposition, 
while  the  Earth  is  moving  from  D  to  E. 

As  the  Earth  moves  from  D  to  F  Mars  moves  in  its  orbit  from  L 


APPARENT  MOTIONS  OF  THE  PLANETS.        189 

to  N.  Its  apparent  place  on  the  celestial  sphere  among  the  stars 
changes  from  Q  to  R.  Its  apparent  motion  is  again  direct — towards 
the  East.  It  is  in  this  way  that  a  superior  planet — one  whose  orbit 
is  outside  of  the  Earth's  orbit — moves  around  the  celestial  sphere. 
Its  general  motion  is  eastwardly  through  long  arcs.  Near  opposition 
its  apparent  motion  is  retrograde  and,  for  a  period,  it  is  stationary. 
It  does  not  then  change  its  place  with  reference  to  stars  near  it. 

The  student  can  study  the  apparent  motion  of  a  superior  planet 
near  conjunction,  or  of  an  inferior  planet  by  constructing  suitable 
diagrams  like  the  foregoing. 

The  superior  planets  (Mars,  Jupiter,  Saturn,  etc.)  make 
the  whole  circuit  of  the  sky  in  long  forward  arcs  with  short 
loops  of  retrogression.  The  inferior  planets  (Mercury  and 
Venus)  do  not  make  the  circuit  of  the  sky.  They  oscillate 
on  either  side  of  the  Sun,  never  going  very  far  away  from 
it.  When  they  are  west  of  the  Sun  they  rise  before  him 
and  are  morning  stars.  When  they  are  east  of  the  Sun 
they  set  after  the  Sun  and  are  evening  stars.  If  Venus  is 
an  evening  star  she  will  approach  the  Sun  nearer  and 
nearer  and  set  nearer  and  nearer  to  the  time  of  sunset. 
By  and  by  she  approaches  so  closely  as  to  be  lost  in  his 
rays  (at  inferior  conjunction — KCS  in  Fig.  123,  where  K 
is  now  the  Earth  and  C  Venus).  In  a  few  days  she  has 
passed  the  Sun  going  westwards  and  rises  before  him  as  a 
morning  star.  The  apparent  motion  of  all  planets  is 
retrograde  when  they  are  nearest  to  the  Earth  and  direct 
when  they  are  farthest  from  us. 

The  apparent  motions  of  all  the  planets  visible  to  the 
naked  eye  were  perfectly  familiar  to  the  ancient  astronomers, 
as  has  been  said.  The  positions  of  the  planets  had  been 
observed  by  them  for  centuries.  But  the  reasons  for  these 
complex  movements  were  not  known.  It  was  everywhere 
believed  that  the  Earth  was  the  centre  of  the  Universe  and 
that  the  Sun,  the  Moon,  the  stars,  and  all  the  planets  were 
made  for  the  sole  benefit  of  mankind.  All  the  explana- 
tions of  the  ancient  philosophers  started  with  the  assump- 


190 


ASTRONOMY. 


tion  that  the  Earth  was  the  centre  of  the  Universe  and 
that  the  Sun  and  all  the  planets  revolved  around  it.  No 
one  thought  of  questioning  this  proposition.  It  was  every- 
where believed. 

PTOLEMY  of  Alexandria  in  Egypt  worked  out  a  theory 
of  the  Universe  on  this  scheme  about  A.D.  140.  It  was  a 
very  ingenious  system  and  it  explained  observed  appear- 
ances fairly  well  so  long  as  the  observations  were  not  very 
accurate. 


FIG.  124. — THE  SYSTEM  OF  THE  WORLD  ACCORDING  TO  PTOLEMY. 


Each  planet  was  supposed  to  move  round  the  circumfer- 
ence of  a  small  circle  called  its  epicycle  (see  the  cut),  while 
the  centre  of  the  epicycle  moved  around  a  larger  circle 
called  the  deferent.  By  taking  the  epicycles  and  the 
deferents  of  suitable  sizes  a  very  fair  representation  of  the 
apparent  motions  of  the  Sun  and  planets  was  made. 

The  swinging  motions  of  Mercury  and  Venus  on  each 
side  of  the  Sun  were  explained  by  their  motions  around 


MOTIONS  OF  THE  PLANETS.  191 

their  epicycles,  which  would  make  them  appear  alternately 
east  and  west  of  the  Sun  if  their  epicycles  moved  round 
their  deferents  at  the  same  rate  that  the  Sun  moved  (see 
the  cut).  The  retrogradations  of  the  superior  planets — 
Mars,  Jupiter,  and  Saturn — were  explicable  in  a  similar 
fashion. 

It  is  not  necessary  to  go  into  details  in  this  matter 
because  PTOLEMY'S  explanation  of  the  Universe  is  not  the 
correct  one.  Still  the  student  should  know  something  of 
a  theory  which  was  believed  by  every  one  from  the  first 
centuries  of  our  Christian  era  until  COPERNICUS  proposed 
the  true  explanation.  It  was  not  until  COPERNICUS  had 
made  long-continued  observations  on  his  own  account  and 
had  given  his  whole  life  to  solving  the  problem  that  it  was 
known  that  the  Sun  and  not  the  Earth  was  the  centre  of  the 
planetary  motions.  He  proposed  this  explanation  in  1543, 
but  it  was  not  generally  accepted  until  the  discoveries  of 
GALILEO  (1610),  about  three  centuries  ago. 

The  theory  of  PTOLEMY  accounted  pretty  well  for  the 
facts  known  in  his  time.  It  represented  the  apparent 
motion  of  the  planets  as  he  observed  them.  But  the 
observations  of  the  Arabian  astronomers  in  Spain  (A.D.  762 
to  1492)  and  of  TYCHO  BRAHE  (pronounced  Tee-ko  Bra-hee) 
in  Denmark  about  1580,  and  especially  the  revelations  of 
GALILEO'S  telescope,  made  PTOLEMY'S  explanation  impossi- 
ble. It  was  not  long  before  it  was  found  that  even  the 
system  proposed  by  COPERNICUS  was  not  entirely  satisfac- 
tory. It  was  certain  that  the  Sun  and  not  the  Earth  was 
the  centre  of  the  planetary  motions,  as  he  had  said.  But 
accurate  observations  soon  made  it  equally  certain  that  the 
planets  did  not  revolve  in  circular  orbits.  They  revolved 
about  the  Sun  in  orbits  nearly  but  not  quite  circular,  in 
curves  like  ovals.  They  certainly  did  not  revolve  in 
circles. 

From    the   time   of  COPERNICUS   (1543)   till    that  of 


192  ASTRONOMY. 

KEPLER  (about  1630)  the  whole  question  of  the  true  system 
of  the  Universe  was  in  debate.  The  circular  orbits  intro- 
duced by  COPERNICUS  also  required  a  complex  system  of 
epicycles  to  account  for  some  of  the  observed  motions  of 
the  planets,  and  with  every  increase  in  accuracy  of  observa- 
tion new  devices  had  to  be  introduced  into  the  system  to 
account  for  the  new  phenomena  observed.  In  short,  the 
system  of  COPERNICUS  accounted  for  so  many  facts  (as  the 
stations  and  retrogradations  of  the  planets)  that  it  could 
not  be  rejected,  and  had  so  many  difficulties  that  without; 
modification  it  could  not  be  accepted. 

—  Describe  how  the  place  of  a  planet  may  be  fixed,  among  the 
fixed  stars,  by  simple  observations.  If  such  observations  are  made 
for  long  periods  the  apparent  paths  of  the  Sun  and  planets  become 
known. — In  what  apparent  paths  do  the  Sun  and  Moon  move? 
Mercury  and  Venus?  The  superior  planets?  Define  the  inferior 
conjunction  of  Venus — the  superior  conjunction  of  Mercury — the 
opposition  of  Jupiter.  Define  the  inferior  planets — the  superior 
planets.  Define  direct  motion — retrograde.  What  was  the  theory  of 
the  Universe  proposed  by  PTOLEMY  in  A.D.  140?  How  long  did  men 
hold  the  belief  that  the  Earth  was  the  centre  about  which  the  planets 
revolved  ?  Who  proposed  the  heliocentric  theory  of  the  solar  system  ? 
At  what  date  ?  What  was  the  shape  of  the  orbits  of  all  the  planets 
in  this  theory  ? 

24.  Kepler's  Laws  of  Planetary  Motion. — KEPLER  (born 
1571,  died  1630)  was  a  genius  of  the  first  order.  He  had 
a  thorough  acquaintance  with  the  old  systems  of  astronomy 
and  a  thorough  belief  in  the  essential  accuracy  of  the 
Copernican  system,  whose  fundamental  theorem  was  that 
the  Sun  and  not  the  Earth  was  the  centre  of  our  system. 
He  lived  at  the  same  time  with  GALILEO,  who  was  the  first 
person  to  observe  the  heavenly  bodies  with  a  telescope  of 
his  own  invention,  and  he  had  the  benefit  of  accurate 
observations  of  the  planets  made  by  TYCHO  BRAHE.  The 
opportunity  for  determining  the  true  laws  of  the  motions 


MOTIONS  OF  THE  PLANETS— KEPLER S  LAWS.     193 

of  the  planets  existed  then  as  it  never  had  before;  and 
fortunately  he  was  able,  through  labors  of  which  it  is  diffi- 
cult to  form  an  idea  to-day,  to  reach  a  true  solution. 

The  Periodic  Time  of  a  Planet. — The  time  of  revolution 
of  a  planet  in  its  orbit  round  the  Sun  (its  periodic  time)  is 


FIG.  125. — JOHN  KEPLER, 
Born  1571,  died  1630. 


determined   by   continuous    observations   of  the  planet's 
course  among  the  stars. 

The  periodic  times  (the  sidereal  periods)  of  the  planets 
were  known  to  KEPLER  from  the  observations  of  the 
ancient  astronomers. 


194  ASTRONOMY. 

Mercury  revolved  about  the  Sun  in  about  88  days==    0. 24  yrs. 
Venus  "          "       "     "       "       225  "  =    0.62    " 

Earth  "          "       "     "       "       365  "  =    1.00    " 

Mars  "          "       "     "       "       687  "  =    1.88    " 

Jupiter          "          "       "     "       l'     4333  "  =  11.86    « 
Saturn          il          "       "     "       "  10,759  "  =  29.46    " 
The   Relative  Distances   of  Planets  from  the   Sun. — 
KEPLER  had  no  way  of  determining  the  absolute  distance 
of  each  planet  from  the  Sun  (its  distance  in  miles),  but  if 
the  distance  of  the  Earth  from  the  Sun  was  taken  as  the 
unit  (1.000)  he  could  determine  the  distances  of  the  other 
planets  in  terms  of  this  unit  in  the  following  way: 


FIG.  126. — METHOD  OP  DETERMINING  How  MUCH  GREATER  THE 
DISTANCE  OF  MARS  FROM  THE  SUN  is  THAN  THE  DISTANCE  OF 
THE  EARTH  FROM  THE  SUN. 

In  the  figure  let  £be  the  Sun,  EE'  the  orbit  of  the  earth,  and  MM 
the  orbit  of  Mars.  When  the  Earth  is  at  E  and  Mars  at  M  the  planet 
is  in  opposition,  i.e.,  it  is  seen  from  the  Earth  in  a  direction  exactly 
opposite  to  the  Sun.  It  is  on  the  meridian  of  the  observer  exactly  at 
midnight.  After  a  hundred  days,  for  example,  Mars  will  have 


MOTIONS  OF  THE  PLANETS— KEPLER 8  LAW 8.    195 

moved  to  M'  and  the  Earth  will  have  moved  to  E'.  The  observer 
will  then  see  the  Sun  in  the  direction  E'  to  8 ;  he  will  see  Mars 
in  the  direction  E'  to  M' .  At  this  time  the  angle  M'E'S  can  be 
measured  with  a  divided  circle,  and  it  therefore  is  a  known  angle. 
The  angle  ESE'  is  known,  because  we  can  calculate  through  what 
angle  the  Earth  will  move  in  100  days,  since  we  know  that  it 
moves  through  360°  in  365£  days.  The  angle  MSM'  is  likewise 
known,  since  we  can  calculate  through  what  angle  Mars  will  move 
in  100  days,  because  we  know  that  Mars  moves  through  360°  in  687 
days.  The  angle  M'SE'  is  therefore  known  because  ESE'  —  M8M' 
=  M'8E'.  Hence  in  the  triangle  M'SE'  we  know  the  two  angles 
marked  in  the  diagram.  E'8M'  is  measured,  M'SE'  is  calculated. 
The  angle  SM'E'  =  180°  —  \E'SM'  +  M'E'8]  because  in  any  plane 
triangle  the  sum  of  the  angles  is  180°.  Hence  in  this  triangle  we 
can  determine  all  three  angles.  We  can  therefore  construct  a 
triangle  of  the  right  shape.  If  we  assume  the  Earth's  distance  SE'  to 
be  1.000  we  can  determine  the  distance  of  Mars  in  terms  of  that 
unit.  If  KEPLER  had  known  the  distance  SE'  in  miles  (as  it  is 
known  nowadays)  then  he  could  have  determined  the  absolute  dis- 
tance, SM',  of  Mars.  As  it  was,  he  could  say  that  if  the  Earth's  dis- 
tance, SE',  was  called  1.000  then  the  distance  of  Mars,  SM',  must 
be  1.52. 

At  different  points  of  the  Earth's  orbit  the  corresponding 
distances  of  Mars  were  determined.  The  same  thing  was 
done  for  the  other  planets  at  different  points  of  their 
orbits.  KEPLER  found  that  if  the  mean  distance  of  the 
Earth  from  the  Sun  was  called  1.000  then  the  mean  dis- 
tances for  all  the  planets  were : 

For  Mercury,  al  =  0.3871;  for  Mars,  at  —  1.5237; 
".  Venus^  «3  =  0.7233;  "  Jupiter,  a,  =  5.2028; 
"  Earth,  a,  =  1.000;  "  Saturn,  a,  =  9.5388. 

The  radius-vector  of  a  planet  is  the  line  that  joins  it  to 
the  Sun. 

KEPLER  made  thousands  and  thousands  of  such  calcula- 
tions and  determined  the  radius- vector  of  Mars  from  the 
Sun  at  all  points  in  its  orbit,  assuming  that  the  Earth's 
average  (mean)  distance  was  1.000.  He  could  therefore 
make  a  map  of  the  orbit  of  Mars  as  in  the  following  figure. 


196  ASTRONOMY. 

In  the  figure  8  is  the  place  of  the  Sun.  At  some  date 
Mars  was  somewhere  along  the  line  SP  (Mars  was  in  a 
certain  known  celestial  longitude).  If  the  distance  of  the 
Earth  from  the  Sun  was  taken  as  the  unit  then  the  dis- 


FIG  127.— THE  OHBIT  OP  A  PLAKET,  P,  ABOUT  THE  SUN,  8. 

tance  of  Mars  was  known  in  terms  of  that  unit.  Mars  was 
at  the  point  P.  At  a  later  time  Mars  was  somewhere  along 
the  radius-vector  $P,,  which  was  in  the  right  longitude. 
Calculation  showed  that  Mars  was  at  the  point  P,.  At 
other  times  Mars  lay  somewhere  along  the  radii- vectores 
SP»  SP,,  SP4,  SPb.  Calculation  showed  that  the  planet 
was  at  the  points  P2,  P3,  P4,  P6.  The  curved  line  joining 
all  these  points  was  the  visible  representation  of  the  orbit 
of  Mars.  The  curve  P,  .  .  .  P6  was  the  true  shape  of 
the  orbit.  Nothing  was  known  of  the  size  of  the  orbit 
except  that  it  was  so  and  so  many  times  larger  than  the 
Earth's;  but  at  any  rate  its  true  shape  was  known.  It 
was  not  a  circle;  it  was  something  like. an  oval.* 

KEPLER'S  next  problem  was  to  determine  what  kind  of 

*  The  real  orbit  of  Mars  is  very  nearly  a  circle  and  the  oval  of  this 
figure  has  been  exaggerated  purposely.  The  curve  that  Mars 
describes  is  not  exactly  circular,  but  it  is  much  less  oval  than 
Fig.  127. 


MOTIONS  OF  THE  PLANETS-KEPLER'S  LA  WS.    197 

a  curve  the  orbit  of  Mars  really  was.  It  was  not  a  circle 
at  any  rate.  He  tried  all  kinds  of  curves  and  finally  dis- 
covered that  Mars,  like  every  other  planet,  moved  around 
the  Sun  in  an  ellipse  and  that  the  Sun  was  not  at  the 
centre  of  the  ellipse,  but  at  one  of  the  foci. 


FIG  128. — AN  ELLIPSE. 

An  ellipse  is  a  curve  such  that  the  sum  of  the  distances 
of  every  point  of  the  curve  from  two  fixed  points  (the  foci) 
is  a  constant  quantity. 

The  student  should  draw  a  number  of  ellipses  for  practice.  Drive 
two  tacks  into  a  board  at  S  and  S'.  Tie  a  string  at  S'  and  the  other 
end  of  the  string  at  8.  Let  the  length  of  the  string  be  SP  -f  P8'- 
Put  a  pencil  at  the  point  P  and  move  the  pencil  round  the  curve, 
always  keeping  the  string  stretched  tight.  Wherever  the  pencil  P 
may  be  the  length  SP  plus  the  length  S'Pis  a  constant  quantity. 
For  every  point  of  the  curve  SP  +  S'P  —  a  constant.  Take  a  string 
of  a  different  length  to  start  with  and  tie  it  to  8  and  S'  and  you  will 
get  an  ellipse  of  a  different  shape.  Put  the  tacks  S  and  8'  nearer 
together  and  the  ellipse  will  be  of  another  shape,  but  it  will  still  be 
an  ellipse. 

ADCP  is  an  ellipse  ;  8  and  3'  are  the  foci.  By  the  definition  of 
an  ellipse  SP -f-  P8'  =  AC,  and  this  is  true  for  every  point.  Sis 
the  focus  occupied  by  the  Sun,  "the  filled  focus."  AS  is  the  least 
distance  of  the  planet  from  the  Sun,  its  perihelion  distance;  and  A 


198 


ASTRONOMY. 


is  the  perihelion,  that  point  nearest  the  Sun.  C  is  the  aphelion,  the 
point  farthest  from  the  Sun.  SA,  SD,  SO,  SB,  SP  are  radii  vectores 
at  different  parts  of  the  orbit.  A  C  is  the  major  axis  of  the  orbit  =  2a. 
The  major  axis  of  the  orbit  is  twice  the  mean  distance  of  the 
planet  from  the  Sun,  a.  BD  is  the  minor  axis,  2b.  The  ratio  of  OS 
to  OA  is  called  the  eccentricity  of  the  ellipse.  By  the  definition  of  the 
ellipse,  again,  BS  +  BS'=  AC  =  2a\  and  BS=  BS'  =  a.  BS*  =  BO* 
-\-~dS*,  or  08=  y  a2  -  6*.  The  eccentricity  of  the  ellipse  is 


OS  _    ^a2-^ 
OA  ~          a 

After  years  of  laborious  calculation  KEPLER  discovered 
three  laws  governing  the  motion  of  the  planets.  (The 
student  should  memorize  these  laws.) 

The  first  law  of  KEPLER  is  — 

/.  Each  planet  moves  around  the  Sim  in  an  ellipse, 
having  the  Sun  at  one  of  its  foci. 

Suppose  the  planet  to  be  at  the  points  P,  P,,  Pa,  Pt, 
P4,  etc.,  at  the  times  T,  7%  T^  T3,  Tt,  etc.,  in  Fig.  129. 


FIG.  129. — KEPLER'S  SECOND  LAW. 

Suppose  the  intervals  of  time  T^  —  T,  T,  —  T»  Tt  —  Tt 
to  be  equal.     KEPLER  computed  the  areas  of  the  surfaces 
P.&P.,  P*SP*  and  found  that  these  areas  were 


MOTIONS  OF  THE  PLANETS— KEPLER 8  LAWS.     199 

equal  also,  and  that  this  was  true  for  each  and  every  planet 
in  every  part  of  its  orbit.  The  second  Jaw  of  KEPLER  is — 

//.  The  radius-vector  of  each  planet  describes  equal  areas 
in  equal  times. 

These  two  laws  are  true  for  each  planet  moving  in  its 
own  ellipse  about  the  Sun. 

For  a  long  time  KEPLER  sought  for  some  law  which 
should  connect  the  motion  of  one  planet  in  its  ellipse  with 
the  motion  of  another  planet  in  its  ellipse.  Finally  he 
found  such  a  relation  between  the  mean  distances  of  the 
different  planets  and  their  periodic  times. 

His  third  law  is: 

///.  The  squares  of  the  periodic  times  of  the  planets  are 
proportional  to  the  cubes  of  their  mean  distances  from  the 
Sun. 

That  is,  if  Tl9  T^  T^  etc.,  are  the  periodic  times  of  the 
different  planets  whose  mean  distances  are  a^  a^  #3,  etc., 
then 


etc.  etc. 

If  T3  and  a3  are  the  periodic  time  and  the  mean  distance 
of  the  Earth  and  if  T3  (=  1  year)  be  taken  as  the  unit  of 
time  and  a3  (=  1.000)  be  taken  as  the  unit  of  distance, 
then  for  any  other  planet  whose  periodic  time  is  T  and 
mean  distance  a 

T*  (its  periodic  time)  :  1  =  a3  (the  cube  of  its  mean  dist.) :  1. 

But  the  periodic  time  of  each  planet  was  already  known 
from  observation  (see  page  193);  hence  its  mean  distance 
can  be  determined  because 

a3  =  T3     or    a=  (T)*. 

If,  in  the  last  equation,  we  substitute  the  values  of  the 
periodic  time  of  each  planet  in  succession,  expressed  in 


200  ASTRONOMY. 

years  and  decimals  of  a  year,  we  shall  obtain  the  valne  of 
a,  its  mean  distance  from  the  Sun,  expressed  in  terms  of 
the  Earth's  mean  distance  =  1.000. 

For  Mercury,  Tl  =  0.24  years  and  al  —  0.39 
"  Venus,  T^=  0.62  "  "  a,  =  0.72 
"  Earth,  I\  =  1.00  "  "  at  =  1.00 
"  Mars,  Tt=  1.88  "  "  a,  =  1.52 
"  Jupiter,  T6  =  11.86  "  "  «6  =  5.20 
"  Saturn,  Tt  =  29.46  "  l<  a,  =  9.54 

KEPLER'S  laws  are  true  for  the  satellites  as  well  as  for 
the  planets.  Mars  has  two  satellites,  PJiobos  and  Deimos, 
that  revolve  in  ellipses  in  periods  T'  and  T"  at  mean  dis- 
tances a'  and  a".  In  their  ellipses  the  line  joining  the 
satellite  to  Mars  sweeps  over  equal  areas  in  equal  times  ; 

and  (TJ  :  (T"Y  =  («')'  :  («")'• 

KEPLER'S  three  laws  give  the  dimensions  of  the  orbits  of 
every  planet  in  terms  of  the  Earth's  distance  =  1.00. 
They  do  not  explain  why  it  is  that  the  planets  follow  these 
orbits  (this  was  not  known  until  the  time  of  NEWTON),  but 
they  enable  us  to  calculate  just  where  any  planet  will  be  in 
its  orbit  at  any  time. 

For  instance,  suppose  that  Mars  was  at  the  place  P  at  the  time  T 
and  we  wished  to  know  where  it  will  be  at  the  time  T'.  The  whole 
area  of  the  ellipse  is  swept  over  by  the  radius-vector  of  Mars  in  1.88 
years.  We  can  calculate  how  much  of  an  area  will  be  swept  over  in 
the  time  T'  —  T.  Then  we  can  calculate  what  the  angle  at  S  of  the 
sector  PSP'  must  be  to  give  this  sector  the  calculated  area.  A  line 
drawn  from  S  to  P'  making  the  calculated  angle  with  SP  will  inter- 
sect the  orbit  at  the  point  P '.  The  planet  will  be  at  the  point  P'  (in 
a  known  celestial  longitude)  at  the  time  T'. 

Elements  of  a  Planet's  Orbit. — When  we  know  a  and  b  (tbe  major  and 
minor  semi-axes)  for  any  orbit,  the  shape  and  size  of  the  orbit  is 
known. 

Knowing  a  we  also  know  T,  the  periodic  time  ;  in  fact  a  is  found 
from  T  by  KEPLER'S  law  III. 

If  we  also  know  the  planet's  celestial  longitude  (L)  at  a  given  epoch, 


MOTIONS  OF  THE  PLANETS— KEPLER'S  LAWS.    201 

say  December  31st,  1850,  we  have  all  the  elements  necessary  for  find- 
ing the  place  of  the  planet  in  its  orbit  at  any  time,  as  has  just  been 
explained. 


FIG.  130.— To  CALCULATE  THE  PLACE  OF  A  PLANET  IN  ITS 
ORBIT  AT  ANY  FUTURE  TIME. 

The  orbit  lies  in  a  certain  plane  ;  this  plane  intersects  the  plane 
of  the  ecliptic  at  a  certain  angle,  which  we  call  the  inclination  i. 
Knowing  i,  the  plane  of  the  planet's  orbit  is  fixed.  The  plane  of  the 
orbit  intersects  the  plane  of  the  ecliptic  in  a  line,  the  line  of  the  nodes. 
Half  of  the  planet's  orbit  lies  below  (south  of)  the  plane  of  the 
ecliptic  and  half  above.  As  the  planet  moves  in  its  orbit  it  must 
pass  through  the  plane  of  the  ecliptic  twice  for  every  revolution. 
The  point  where  it  passes  through  the  ecliptic  going  from  the  south 
half  to  the  north  half  of  its  orbit  is  the  ascending  node;  the  point 
where  it  passes  through  the  ecliptic  going  from  north  to  south  is  the 
descending  node  of  the  planet's  orbit.  If  we  have  only  the  inclina- 
tion given,  the  orbit  of  the  planet  may  lie  anywhere  in  the  plane 
whose  angle  with  the  ecliptic  is  ».  If  we  fix  the  place  of  the  nodes, 
or  of  one  of  them,  the  orbit  is  thus  fixed  in  its  plane.  This  we  do 
by  giving  the  (celestial)  longitude  of  the  ascending  node  Q . 

Now  everything  is  known  except  the  relation  of  the  planet's  orbit 
to  the  sun.  This  is  fixed  by  the  longitude  of  the  perihelion,  or  P. 

Thus  the  elements  of  a  planet's  orbit  are  : 

*,  the  inclination  to  the  ecliptic,  which  fixes  the  plane  of  the 
planet's  orbit; 

Q ,  the  longitude  of  the  node,  which  fixes  the  position  of  the  line  of 
intersection  of  the  orbit  and  the  ecliptic; 


202  ASTRONOMY. 

P,  the  longitude  of  the  perihelion,  which  fixes  the  position  of  the 
major  axis  of  the  planet's  orbit  with  relation  to  the  Sun ,  and  hence 
in  space; 

a  and  e,  the  mean  distance  and  eccentricity  of  the  orbit,  which  fix 
the  shape  and  size  of  the  orbit  (see  page  198); 

T  and  M,  the  periodic  time  and  the  longitude  at  the  epoch,  which 
enable  the  place  of  the  planet  in  its  orbit,  and  hence  in  space,  to  be 
fixed  at  any  future  or  past  time. 

The  elements  of  the  older  planets  of  the  solar  system  are  now 
known  with  great  accuracy,  and  their  positions  for  two  or  three  cen- 
turies past  or  future  can  be  predicted  with  a  close  approximation  to 
the  accuracy  with  which  these  positions  can  be  observed. 

Moreover  it  was  proved  by  two  great  French  astronomers  (LA- 
GRANGE  and  LAPLACE)  about  a  hundred  years  ago  that  all  the 
planets  would  always  continue  to  revolve  in  or  near  the  plane  of  the 
ecliptic;  that  the  eccentricity  of  each  orbit  might  vary  within  narrow 
limits,  but  could  never  depart  widely  from  its  present  value,  and 
finally  that  the  mean-distances  of  the  planets  would  always  remain 
the  same  as  now.  The  Earth,  for  example,  will  always  remain  at  the 
same  average  distance  from  the  Sun  as  now,  though  by  a  change  in 
the  eccentricity  its  least  and  greatest  distances  from  the  Sun  may  be 
slightly  greater  or  less  than  at  present.  Hence  there  can  never  be 
any  great  changes  in  the  seasons  of  the  Earth  due  to  a  change  in  its 
distance  from  the  Sun. 

If  the  mean-distances  of  the  planets  remain  essentially  unchanged 
their  periodic  times  will  also  remain  unchanged,  by  the  3d  law  of 
KEPLER,  so  long  as  we  consider  the  planets  as  rigid  solids. 

—  What  is  a  planet's  periodic-time?  How  can  the  relative  dis- 
tances of  the  planets  from  the  Sun  be  determined  ?  What  are  the 
three  laws  of  planetary  motion  discovered  by  KEPLER  ?  Define  an 
ellipse.  Do  KEPLER'S  laws  explain  why  the  planets  move  in  elliptic 
orbits?  why  their  radii- vectores  describe  equal  areas  in  equal  times? 
why  for  any  two  planets  T*  :  TJ  =  as  :  aS?  What  are  the  elements 
of  a  planet's  orbit  ? 


CHAPTEE   X. 

UNIVERSAL   GRAVITATION. 

25.  The  Discoveries  of  Sir  ISAAC  NEWTON. — Before  the 
time  of  Sir  ISAAC  NEWTON  very  little  was  known  of  the 
laws  that  govern  the  motion  of  bodies  on  the  Earth.  A 
stone  dropped  from  the  hand  falls  to  the  ground.  Why  ? 
NEWTON'S  answer  was  that  the  Earth  attracted  the  stone 
downwards  somewhat  as  a  magnet  attracts  iron  to  itself. 
The  Earth  itself  was  made  up  of  stones  and  soil.  Why  did 
not  the  stone  attract  the  Earth  upwards?  NEWTON'S 
answer  was  that  the  stone  did,  in  fact,  attract  the  Earth. 
But  as  the  Earth  had  a  mass  of  millions  of  tons  and  the 
stone  a  mass  of  only  a  few  pounds  the  motion  of  the  Earth 
upwards  towards  the  stone  was  very  small  compared  to  the 
motion  of  the  stone  downwards  to  the  Earth.  It  was  too 
small  to  be  appreciable — but  the  Earth  moved  nevertheless. 
The  attraction  was  in  proportion  to  the  attracting  mass,  he 
said. 

Each  particle  of  a  huge  mass,  like  that  of  the  Earth, 
would  attract  the  stone,  and  the  whole  of  the  Earth's 
attraction  would  be  the  sum  of  all  the  particular  attrac- 
tions. The  stone  would  also  attract  each  one  of  the 
Earth's  particles,  but  as  they  were  all  joined  together  it 
could  move  no  one  of  them  without  moving  them  all.  If 
the  Earth  attracted  a  stone  near  its  surface  why  should  it 
not  attract  the  Moon  in  the  sky  ?  The  Moon  would  be 
attracted  less  because  it  was  distant,  but  it  would  certainly 
be  attracted,  he  said.  There  were  reasons  for  believing 

203 


204 


ASTRONOMY. 


that  attractions  grew  less  in  proportion  to  the  square  of  the 
distance,  not  in  proportion  to  the  simple  distance. 

His  reasoning  was  something  like  this:  We  see  that  there 
is  a  force  acting  all  over  the  Earth  by  which  all  bodies  are 
drawn  towards  its  centre.  This  force  is  called  gravity.  It 
extends  to  the  tops  not  only  of  the  highest  buildings,  but 
of  the  highest  mountains.  How  much  higher  does  it 


FIG.  131. 

A  stone  in  a  sling  is  whirled  round  in  the  direction  of  the  arrows  in  the 
circle  CBA.  At  A  the  string  breaks  and  the  stone  flies  away  in  the 
tangent  AD.  It  would  move  away  in  that  direction  forever  if  the  Earth 
did  not  attract  it  downwards 

extend  ?  Why  should  it  not  extend  to  the  Moon  ?  If  it 
does,  the  Moon  would  tend  to  drop  towards  the  Earth,  just 
as  a  stone  thrown  from  the  hand  drops.  As  the  Moon 
moves  round  the  Earth  in  her  monthly  course,  there  must 
be  some  force  drawing  her  towards  the  Earth;  else  she 
would  fly  entirely  away  in  a  straight  line  just  as  a  stone 
thrown  from  a  sling  would  fly  away  in  a  straight  line  if  the 


FIG.  132.— SIR  ISAAC  NEWTON. 
Born  1642 ;  died  1727. 


205 


206  ASTRONOMY. 

Earth  did  not  attract  it.  Why  should  not  the  force  which 
makes  the  stone  fall  be  the  same  force  which  keeps  the 
Moon  in  her  orbit  ? 

To  answer  this  question,  it  was  necessary  to  calculate 
the  intensity  of  the  force  which  would  keep  the  Moon  her- 
self in  her  orbit,  and  to  compare  it  with  the  intensity  of 
gravity  at  the  Earth's  surface.  It  had  long  been  known 
that  the  distance  of  the  Moon  was  about  sixty  radii  of  the 
Earth.  If  this  force  diminished  as  the  inverse  square  of 
the  distance,  then  at  the  Moon  it  would  be  only  ^-^  as 
great  as  at  the  Earth's  surface. 

Experiments  at  the  Earth's  surface  had  proved  that  a 
body  fell  16  feet  in  a  second  of  time.  The  Moon  in  her 
orbit  ought  then  to  fall  towards  the  Earth  (that  is,  ought  to 
bend  away  from  a  straight  line)  by  ¥^¥7  part  of  16  feet  in 
each  and  every  second,  or  the  Moon  should  bend  away  from 
a  straight  line  (a  tangent  to  her  orbit)  by  about  TV  part  of 
an  inch  every  second.  Now  the  size  of  the  Moon's  orbit 
was  known  and  its  curvature  was  known.  It  was  found 
that  the  orbit  of  the  Moon  did,  in  fact,  deflect  from  the 
tangent  to  the  orbit  by  -fa  part  of  an  inch  per  second. 
NEWTON  proved  this  point  by  calculation,  and  from  that 
time  forward  he  felt  sure  that  the  force  that  kept  the  Moon 
in  its  orbit  about  the  Earth  was  a  force  of  the  same  kind 
as  the  gravity  that  made  a  stone  fall  to  the  Earth,  and  that 
it  was  this  very  same  force  that  kept  all  the  planets  in  their 
orbits  about  the  Sun. 

To  prove  that  his  idea  was  right  it  was  necessary  to  prove 
that  if  the  Sun  attracted  the  planets  just  as  the  Earth 
attracted  the  Moon  the  laws  of  KEPLER  would  be  a  neces- 
sary consequence.  NEWTON  made  such  a  proof.  lie 
proved  strictly  and  mathematically  that  any  two  bodies 
which  attracted  each  other  in  proportion  to  their  masses 
and  inversely  as  the  square  of  their  distances  apart  would 
obey  laws  like  those  of  KEPLER.  If  one  of  the  bodies  was 


UNIVERSAL   GRAVITATION.  207 

very  large  (like  the  San)  and  the  other  much  smaller  (like 
one  of  the  planets)  then  it  necessarily  followed  from  the 
single  law  of  gravitation  that: 

I.  The  planet  would  revolve  about  the  Sun  in  an  ellipse 
(or  in  one  of  a  set  of  curves  of  the  same  sort).  II.  The 
radius- vector  of  the  planet  would  describe  equal  areas  in 
equal  times.  And  he  further  proved  that  if  there  were 
two  planets  in  the  system  the  following  law  would  be  very 
nearly  true:  III.  The  squares  of  their  periodic  times  would 
be  proportional  to  the  cubes  of  their  mean  distances  from 
the  Sun.  These  are  the  three  laws  which  KEPLER  deduced 
from  observation.  All  the  planets  in  the  solar  system  obey 
these  laws.  All  the  planets  obey  the  law  of  gravitation 
therefore. 

KEPLER'S  laws  were  proved  to  be  true  by  observation.  NEWTON 
showed  that  if  any  planet  moved  about  the  sun  so  that  its  radius- 
vector  described  equal  areas  in  equal  times  then  the  planet  obeyed  a 
force  that  was  directed  always  to  the  sun  as  a  centre  of  force.  If  the 
path  of  any  planet  was  an  ellipse  (or  if  it  were  a  parabola  or  hyper- 
bola) then  the  central  force  must  vary  inversely  as  the  square  of  the 
distance,  and  could  vary  in  no  other  way.  If  all  the  planets  were 
bound  together  (as  they  are)  by  KEPLER'S  third  law,  then  all  the  plan- 
ets are  acted  on  by  one  and  the  same  kind  of  force.  The  amount  of 
force  acting  on  any  planet  depends  on  its  distance  from  the  Sun  and 
on  the  mass  of  the  Sun.  Observations  fixed  the  length  of  each  plan- 
et's year  and  its  distance  from  the  Sun. 

From  these  data  the  mass  of  the  Sun  could  be  calculated  in  terms 
of  the  Earth's  mass.  Not  only  were  these  things  true  for  all  the 
planets  ;  they  governed  the  motions  of  satellites  about  their  primary 
planet.  The  Moon  revolves  about  its  primary,  the  Earth,  in  obe- 
dience to  its  attraction  ;  but  it  is  likewise  attracted  by  the  Sun  and 
hence  its  orbit  is  perturbed.  NEWTON  calculated  perturbations  of 
the  Moon's  motion  that  had  been  known  as  facts  of  observation  since 
the  time  of  HIPPARCHUS,  and  others  that  had  been  observed  by  TYCHO 
BRAHE  and  FLAMSTEED,  and  he  accounted  for  all  these  observed  facts 
by  his  theory.  He  also  calculated  some  of  the  perturbations  of  the 
path  of  one  planet  by  the  attraction  of  other  planets. 

Up  to  NEWTON'S  day  the  motions  of  comets  had  been  simply  mys- 
terious. He  showed  that  they  moved  according  to  KEPLER'S  laws, 


208  ASTRONOMY. 

usually  in  parabolas,  not  in  ellipses.  He  calculated  the  shape  that  a 
rotating  fluid  mass  should  assume  and  from  this  deduced  the  figure 
of  the  Earth.  He  showed  that  it  was  a  spheroid,  not  a  sphere,  and 
proved  that  the  precession  of  the  equinoxes,  observed  as  a  fact  by 
HIPPARCHUS,  and  unexplained  since  his  time,  was  a  mere  result  of 
the  spheroidal  shape  of  the  Earth.  The  Tides — another  mystery — 
were  explained  by  NEWTON  as  a  result  of  the  Moon's  attraction  of 
the  waters  of  the  Ocean. 

His  discoveries  in  pure  mathematics  are  only  second  in  importance 
to  his  discoveries  in  celestial  mechanics.  The  binomial  theorem  was 
discovered  by  him  (it  is  engraved  on  his  tomb  in  Westminster 
Abbey).  The  Differential  Calculus  is  his  invention.  He  made  most 
important  discoveries  in  optics  also. 

The  epigram  of  the  English  poet  POPE  expresses  the  feeling  of 
awed  amazement  with  which  the  men  of  his  own  time  regarded  this 
mighty  genius  : 

Nature  and  Nature's  laws  lay  hid  in  Night : 
God  said  let  Newton  be — and  all  was  Light. 

Let  us  see  what  NEWTON  thought  of  himself.  Towards  the  end 
of  his  life  he  said,  "  I  know  not  what  the  world  will  think  of  my 
labors,  but  to  myself  it  seems  that  I  have  been  but  as  a  child  playing 
on  the  seashore  ;  now  finding  some  pebble  rather  more  polished  and 
now  some  shell  rather  more  agreeably  variegated  than  another,  while 
the  immense  ocean  of  Truth  extended  itself,  unexplored,  beyond  me." 

In  science  his  name  is  venerated  and  honored  by  all  those  who  can 
appreciate  his  marvellous  genius.  His  greatest  effect  on  Mankind 
has  been  to  set  before  them  a  new  path  for  their  thoughts  to  follow. 
Since  his  day  men  have  a  new  view-of-the-world,  and  his  discoveries 
have  influenced  the  thoughts,  beliefs,  and  ideals  of  men  and  nations 
as  powerfully  and  as  effectively  as  those  of  PLATO,  ARISTOTLE,  CO- 
PERNICUS, and  GALILEO.  We  should  not  now  think  as  we  all  do  if 
our  thoughts  did  not  run  in  channels  first  opened  by  him. 

All  the  motions  of  all  the  bodies  in  the  solar  system  were 
deduced  by  NEWTON  from  one  single  law — the  law  of 
Universal  Gravitation.  The  discoveries  of  PTOLEMY,  of 
COPERNICUS,  of  KEPLER,  and  of  all  other  astronomers  were 
nothing  but  special  cases  of  one  universal  law.  PTOLEMY 
and  other  great  astronomers  before  his  time  had  mapped 
out  the  apparent  courses  of  the  planets  in  the  sky  with 


UNIVERSAL   GRAVITATION.  209 

diligence  and  with  accuracy.  COPERNICUS  had  shown 
that  these  apparent  paths  were  described  because  the 
real  centre  of  the  motion  was  the  Sun.  KEPLER  had 
proved  that  the  paths  of  the  planets  about  the  Sun  were  not 
circles  as  COPERNICUS  supposed,  but  ellipses;  and  he  gave 
the  laws  according  to  which  the  planets  moved  in  their  real 
orbits. 

NEWTON  started  with  the  simple  fact  of  gravity  (Latin 
gravitas  =  heaviness).  He  said  a  body  is  heavy  because 
the  Earth  attracts  it.  The  Earth  (like  every  mass)  at- 
tracts all  other  bodies  in  the  Universe,  the  nearer  bodies 
more,  the  distant  bodies  less.  The  attraction  is  directly 
proportional  to  the  mass;  it  is  inversely  proportional  to  the 
square  of  the  distance.  If  this  law  is  true  everywhere  (as 
experiment  proves  it  to  be  true  on  the  Earth)  then  all 
KEPLER'S  laws  are  a  necessary  consequence  of  it.  One 
single  law  accounts  for  every  motion  in  the  solar  system. 
Probably  this  law  accounts  for  all  the  motions  of  the  stars 
also. 

The  student  should  memorize  the  law  of  universal  gravi- 
tation in  the  form  that  NEWTON  gave  to  it — as  follows: 

Every  particle  of  matter  in  the  universe  attracts  every 
other  particle  with  a  force  directly  as  the  masses  of  the  two 
particles  and  inversely  as  the  square  of  the  distance  between 
them. 

To  thoroughly  understand  the  discoveries  of  NEWTON  it  is  neces- 
sary to  study  Mechanics  or  the  science  that  treats  of  the  action  of 
forces  on  bodies.  This  science  requires  a  mathematical  treatment 
too  difficult  and  too  long  to  be  given  here.  After  the  Mechanics  of 
terrestrial  bodies  is  understood  it  must  be  applied  to  the  special  case 
of  the  heavenly  bodies—  Celestial  Mechanics.  Only  the  barest  out- 
line of  NEWTON'S  achievements  can  be  given  in  this  place.  The  fol- 
lowing paragraphs  may  help  the  student  to  understand  the  nature 
of  the  questions  involved. 

If  we  represent  by  m  and  mf  the  masses  of  two  attracting  bodies, 
we  may  conceive  the  body  m  to  be  composed  of  m  particles,  and  the 
other  body  to  be  composed  of  m'  particles.  Let  us  conceive  that 


210  ASTRONOMY. 

each  particle  of  one  body  attracts  each  particle  of  the  other  with  a 
force  that  varies  as  —  .  Then  every  particle  of  m  will  be  attracted 
by  each  of  the  m'  particles  of  the  other,  and  therefore  the  attractive 
force  on  each  of  the  m  particles  will  vary  as  2  .  Each  of  the  m 
particles  being  equally  subject  to  this  attraction,  the  total  attractive 
force  between  the  two  bodies  will  vary  as  —  j-. 

Each  of  the  two  masses  attracts  the  other  by  a  force  varying 


If  a  straight  stiff  rod  whose  length  was  r  could  be  slipped  in 
between  the  two  masses  m  and  m',  the  pressure  on  either  end  of 


-m' 


FIG.  133. 

the   rod  would  be  the  same.     It  would  be  a  pressure  proportional 
mm' 

te^r-. 

When  a  given  force  acts  upon  a  body,  it  will  produce  less  motion 
the  larger  the  body  is,  the  accelerating  force  being  proportional  to 
the  total  attracting  force  divided  by  the  mass  of  the  body  moved. 
Therefore  the  accelerating  force  which  acts  on  the  body  m',  and 

which  determines  the  amount  of  motion,  will  be  — ;  and  conversely 
the  accelerating  force  acting  on  the  body  m  will  be  represented  by 
the  fraction  — .  If  m  is  very  large  (as  in  the  case  of  the  San)  and 

if  m'  is  relatively  small  (as  in  the  case  of  a  planet),  the  motion  of  the 
planet  will  be  determined  by  the  Sun's  accelerating  force  while  the 
Sun  will  be  but  little  affected  by  the  accelerating  force  of  the  planet. 

It  makes  no  difference  at  all  of  what  substances  m  and  m'  are 
made  up.  A  mass  of  gas  (as  a  comet)  attracts  in  proportion  to  its 
quantity  of  matter,  just  as  amass  of  lead  attracts  in  proportion  to 
its  quantity  of  matter. 

It  is  in  this  respect,  especially,  that  the  force  of  gravitation  differs 
from  a  force  like  magnetism.  A  magnet  will  attract  iron  but  not 
wood.  But  both  wood  and  iron  are  heavy. 

The  attraction  of  a  spherical  body  on  a  particle  outside  of  itself 
is  the  same  as  if  the  whole  mass  of  the  spherical  body  were  con- 


UNIVERSAL   GRAVITATION.  211 

centrated  at  its  centre.  We  may  treat  the  problems  of  Celestial 
Mechanics  as  if  the  Sun  and  all  the  planets  were  mere  points,  the 
whole  mass  of  each  body  being  concentrated  at  their  centres.  The 
attraction  of  the  Earth  for  bodies  on  its  surface  is  the  same  as  if  the 
earth  were  a  mere  point,  its  whole  mass  being  concentrated  at 
its  centre. 

A  word  may  be  said  on  the  variation  of  forces  inversely  as  the 
square  of  the  distance.  Suppose  we  take  the  force  of  gravitation. 
At  a  distance  of  one  radius  of  the  Earth  from  the  Earth's  centre  (at 
the  Earth's  surface)  let  us  call  its  intensity  one  ;  at  a  distance  of  two 
radii  (some  4000  miles  above  the  Earth's  surface  therefore)  it  will 
be  ^  ;  at  a  distance  of  3  radii  it  will  be  £  ;  and  so  on. 

Distances  =1,2,3,4,5,     6    ....  100      ...      1000 
Forces       =  1  ,  i  ,  i  ,  A  »  *V  .  A  »  •  •  •  nd™  •;•'••  nsoW 
An  excellent  practical  example  of  a  quantity  that  varies  inversely 
as  the  square  of  the  distance  may  be  had  by  watching  the  headlight 
of  a  tram-car  as  it  approaches  you.     When  it  is  five  blocks  off  the 
intensity  of  the  light  is  ^th,  four  blocks  off  y'gth,  three  blocks  £, 
two  blocks  |  of  the  intensity  at  a  distance  of  a  block.     Gravitation 
varies  according  to  a  similar  law. 

Gravitating  force  seems  to  go  out  from  every  particle  of  matter  in 
the  Universe  in  all  directions  somewhat  as  rays  of  light  stream  out 
in  all  directions  from  a  lamp.  It  streams  out  in  straight  lines.  What- 
ever  is  in  its  way  is  attracted.  If  a  planet  is  there  it  attracts  the 
planet.  If  nothing  is  there  no  attraction  is  exerted  on  empty  space. 
The  rays  of  gravitation  (so  to  speak)  pass  directly  through  a  body  and 
a  second  body  beyond  it  is  attracted  just  as  if  the  first  body  were  not 
there.  There  is  no  gravitational  shadow,  as  it  were. 

A B C 

If  A  were  a  lamp  and  B  and  C  two  screens,  the  screen  B  would  be 
lighted  and  the  screen  C  would  be  in  shadow.  But  if  A  is  a  heavy 
body  it  will  attract  a  body  at  B  and  another  body  C  beyond  it  just  as 
if  B  were  not  there. 

Moreover,  the  storehouse  of  gravitational  attraction  in  a  heavy  body 
is  never  exhausted.  The  sun  attracts  a  planet  at  a  certain  distance 
just  as  much  in  July  as  in  the  preceding  January,  just  as  much  in 
1907  as  in  1620. 

It  requires  time  for  the  light  of  the  Sun  to  travel  across  the  space 
that  separates  it  from  the  Earth.  A  beam  of  light  leaves  the  Sun 
and  does  not  arrive  at  the  Earth  for  8m  19%  it  does  not  arrive  at 
Jupiter  for  43m  15s.  It  takes  these  times  to  pass  over  the  intervening 


212  ASTRONOMY. 

spaces.  But  the  gravitating  effect  of  the  Sun  traverses  these  spaces 
instantaneously,  so  far  as  we  now  know.  When  gravitation  is  con- 
sidered in  this  way,  as  a  force  inherent  in  a -body,  as  sourness  is  in- 
herent in  a  fruit,  a  recital  of  its  properties  sounds  like  a  fairy-tale. 
The  explanation  of  gravitation  is  not  yet  known.  This  force,  like 
the  force  of  magnetism  and  other  forces,  is  a  mystery.  When  its  ex- 
planation comes  to  be  known  it  will  probably  be  found  that  a  heavy 
body  must  not  be  considered  to  be  in  empty  space,  but  in  a  space 
filled  with  some  substance  like  the  ether  which  transmits  light.  The 
body  influences  the  ether  and  sets  up  strains  and  stresses  within  it. 
These  stresses  are  transmitted  in  all  directions  with  immense  (prob- 
ably not  infinitely  great)  velocities.  When  these  stresses  meet  a 
second  body  they  act  upon  it  to  produce  the  phenomena  of  gravita- 
tion. 

A  word  may  also  be  said  as  to  the  intensity  of  the  force  of  gravi- 
tation. The  popular  notion  is  that  gravitation  is  a  very  powerful 
force.  This  is  because  we  live  on  an  earth  which  is  very  large  in 
comparison  to  our  own  size,  and  to  the  sizes  of  objects  that  we  use  in 
our  daily  life.  In  reality  gravitation  may  be  called  a  feeble  force 
compared  to  such  a  force  as  the  expansion  of  water  when  it  freezes 
and  bursts  the  stout  pipes  in  which  it  is  contained.  Two  masses  M 
and  M' ,  each  weighing  415,000  tons,  a  mile  apart,  attract  each  other 
with  a  force  of  one  pound.  Imagine  two  huge  cubes  of  iron,  each 
weighing  415,000  tons.  If  at  a  mile's  distance  they  only  exert  a  force 
of  one  pound  we  must  decide  that  the  force  of  gravitation  is  feeble 
rather  than  powerful.  If  M  and  M'  were  two  miles  apart  their  mu- 
tual attraction  would  be  only  four  ounces.  If  M  was  doubled  in  size, 
their  attraction  at  one  mile's  distance  would  be  two  pounds  ;  if  both 
M  and  M'  were  doubled  their  attraction  would  be  four  pounds,  and 
so  on.  These  effects  one  would  call  small  rather  than  large. 

The  discoveries  of  NEWTON  in  relation  to  the  force  of  gravitation 
that  binds  the  planets  together  and  that  determines  every  circum- 
stance of  every  motion  of  everything  on  the  Earth  lead  to  conclu- 
sions like  those  just  set  down.  What  the  true  nature  of  this  force 
is  we  do  not  know  any  more  than  we  know  the  true  nature  of  the 
forces  of  chemical  affinity  and  the  like.  No  doubt  a  complete  under- 
standing of  it  will  some  day  be  reached,  and  what  now  seems  mar- 
vellous will  then  be  simple.  There  is  no  doubt  that  the  motions  of 
every  particle  on  the  Earth  and  of  every  planet  in  the  solar  system 
are  obedient  to  this  law.  The  simple  proof  is  that  the  motions  of 
planets,  comets,  and  of  many  stars  have  been  calculated  beforehand 
on  this  theory  and  that  observation  has  subsequently  verified  the 
predictions.  The  pages  of  the  Nautical  Almanac  (see  page  150)  are 


UNIVERSAL  GRAVITATION. 


213 


nothing  but  a  series  of  such  predictions  that  are  afterwards  verified 
over  and  over  again  in  the  minutest  particular.  The  place  that  a 
planet  will  occupy  in  the  sky  a  century  hence  can  be  predicted 
nearly  as  accurately  as  the  planet  can  then  be  observed.  Not  only 
this,  but  the  paths  of  thousands  of  projectiles  to  be  fired  from  can- 
non have  been  calculated  beforehand,  and  these  predictions  have  been 
subsequently  verified  by  experiment.  Every  swing  of  a  pendulum 
and  every  fall  of  a  heavy  body  u  obedient  to  this  law,  and  in  thou- 
sands and  thousands  of  similar  cases  the  law  has  been  accurately 
verified  by  experiment. 

Mutual  Actions  of  the  Planets  —  Perturbations.  —  KEPLER'S  laws 
would  be  accurately  followed  in  any  system  of  only  two  heavy 
bodies,  as  the  Sun  and  any  one  planet,  Mars  for  example.  If  a  third 
body  exists,  the  Earth  for  instance,  it  will  attract  the  Sun  and  also 
Mars.  The  Sun  and  Mars  will  likewise  attract  the  Earth.  The 
motion  of  Mars  about  the  Sun  will  not  be  exactly  the  same  in  a  sys- 
tem of  three  bodies  as  in  a  system  of  two. 
The  mass  of  the  Sun  is  so  very  much 
greater  than  the  mass  of  the  Earth  that 
Mars  will  travel  in  an  orbit  almost  the 
same  as  its  undisturbed  orbit  —  almost,  but 
not  quite.  The  Earth  will  produce  slight 
disturbances  —  perturbations  they  are  called 
—  in  the  orbit  of  Mars,  and  these  perturba- 
tions can  be  exactly  calculated  from  NEW- 
TON'S law.  The  orbit  of  the  Earth  will 
also  be  perturbed  by  Mars. 

Each  of  the  planets  will  act  on  every 
one  of  the  other  planets  to  alter  its  motion. 
These  disturbances  in  the  solar  system  are 
small,  because  the  Sun's  mass  is  so  very 
large  compared  to  the  mass  of  the  dis- 
turbing body.  Even  Jupiter,  the  largest 
of  the  planets,  has  a  mass  less  than  y^Vu  of 
the  Sun's  mass. 


._  A  PENDULUM 
AT  REST  HANGS  VER- 


The  Vertical  Line.—  The  direction 
np  and  down,  the  vertical  direction,  is 
defined  for  any  observer  by  the  line 
in  which  a  pendulum  at  rest  hangs.  The  pendulum  is  at- 
tracted hy  the  whole  Earth  and  if  the  Earth  were  a  sphere 
it  would  always  point  to  the  Earth's  centre.  As  the  Earth 


ASTRONOMY. 


is  a  spheroid  (its  meridians  being  ellipses  and  not  circles) 
a  pendulum  at  rest  at  any  point  of  the  Earth's  surface  does 
not  point  exactly  to  the  centre,  although  its  direction  is 


FIG.  135. — A  PENDULUM  AT  REST  ON  A  SPHERICAL  EARTH 

POINTS  NEARLY  TO  THE  CENTRE  OF  THE  EARTH. 

never  far  from  that  of  the  Earth's  radius.  (The  radius  of 
the  Earth  and  the  pendulum  never  make  an  angle  of  more 
than  12'  of  arc — a  fifth  of  a  degree — with  each  other.) 

The  zenith  of  an  observer  may  now  be  defined  as  that 
point  over  his  head  where  a  pendulum  at  rest  at  his  station 
would  meet  the  celestial  sphere  if  the  pendulum  were  in- 
definitely long.  A  pendulum  at  rest  always  lies  in  the  line 
of  joining  an  observer's  zenith  and  nadir. 

REMARKS  ON  THE  THEORY  OF  GRAVITATION. 

The  real  nature  of  the  discovery  of  NEWTON  is  frequently 
misunderstood.  Gravitation  is  sometimes  spoken  of  as  if 
it  were  a  theory  of  NEWTON'S,  now  very  generally  received, 


UNIVERSAL  GRAVITATION. 

but  still  liable  to  be  ultimately  rejected  as  a  great  many 
other  theories  have  been. 

NEWTON  did  not  discover  any  new  force,  but  only  showed 
that  the  motions  of  the  heavenly  bodies  could  be  accounted 
for  by  a  force  which  we  all  know  to  exist.  Gravitation  is 
the  force  which  makes  all  bodies  here  at  the  surface  of  the 
Earth  tend  to  fall  downward;  and  if  any  one  wishes  to 
subvert  the  theory  of  gravitation,  he  must  begin  by  proving 
that  this  force  does  not  exist.  This  no  one  would  think  of 
doing.  What  NEWTON  did  was  to  show  that  this  force, 
which,  before  his  time,  had  been  recognized  only  as  acting 
on  the  surface  of  the  Earth,  really  extended  to  the 
heavens,  and  that  it  resided  not  only  in  the  Earth  itself, 
but  in  the  heavenly  bodies  also,  and  in  each  particle  of 
matter,  wherever  situated.  To  put  the  matter  in  a  terse 
form,  what  NEWTON  discovered  was  not  gravitation,  but 
the  universality  of  gravitation. 

—  What  was  the  principal  work  of  PTOLEMY  and  his  predeces- 
sors ?  What  was  the  discovery  of  COPERNICUS?  What  was  KEP- 
LER'S discovery?  What  was  the  greatest  discovery  of  NEWTON? 
Give  NEWTON'S  law  of  universal  gravitation  in  his  own  words.  Did 
NEWTON  discover  gravitation  ?  What,  in  fine,  was  his  discovery  ? 
Define  the  zenith  of  an  observer — his  nadir. 


CHAPTER  XL 
THE  MOTIONS  AND  PHASES  OF  THE  MOON. 

26.  The  Moon  makes  the  circuit  of  the  heavens  once  in 
each  (lunar)  month.  She  revolves  in  a  nearly  circular 
orbit  around  the  Earth  (not  the  Sun)  at  a  mean  distance 
of  240,000  miles.  At  certain  times  the  new  Moon,  a 
slender  crescent,  is  seen  in  the  west  near  the  setting  Sun. 
On  each  succeeding  evening  we  see  her  further  to  the  east, 
so  that  in  two  weeks  she  is  exactly  opposite  the  Sun,  rising 
in  the  east  as  he  sets  in  the  west.  Continuing  her  course 
two  weeks  more,  she  has  approached  the  Sun  from  the  west, 
and  is  once  more  lost  in  his  rays.  At  the  end  of  twenty- 
nine  or  thirty  days,  we  see  her  again  emerging  as  new 
Moon,  and  her  circuit  is  complete.  The  Sun  has  been 
apparently  moving  towards  the  east  among  the  stars  during 
the  whole  month  at  the  rate  of  1°  daily  (see  page  165),  so 
that  during  the  interval  from  one  new  Moon  to  the  next 
the  Moon  has  to  make  a  complete  circuit  relatively  to  the 
stars,  and  to  move  forward  some  30°  further  to  overtake 
the  Sun.  The  revolution  of  the  Moon  among  the  stars  is 
performed  in  about  27£  days,  so  that  if  the  Moon  is  very 
near  some  star  on  March  1,  for  example,  we  shall  find  her 
in  the  same  position  relative  to  the  star  on  March  28. 

The  Moon's  revolution  relative  to  the  stars  is  performed 
in  27£  days;  relative  to  the  Sun  in  29£  days.  Her  periodic 
time  in  her  orbit  about  the  Earth  is  27£  days  therefore. 

Phases  of  the  Moon. — The  Moon  is  an  opaque  body  and 
is  formed  of  materials  something  like  the  rocks  and  soils  of 

216 


MOTIONS  AND  PHASES  OF  THE  MOON.    217 


the  Earth.  Like  the  planets,  she  does  not  shine  by  her  own 
light,  but  by  the  light  of  the  Sun,  which  is  reflected  from 
her  surface  much  as  sunlight  would  be  reflected  from  a 
rough  mirror.  As  the  Moon,  like  the  Earth,  is  a  sphere, 
only  half  of  her  globe  can  be  illuminated  at  a  time  —  namely, 
that  half  turned  towards  the  San. 


M 


FIG.  136. — THE  MOON  (M)  IN  HER  ORBIT  ROUND  THE  EARTH  (E). 

Half  of  each  body  is  illuminated  by  the  Sun.  The  Sun  is  not  shown  in 
the  drawing.  If  it  were  to  be  inserted  it  would  have  to  be  on  the  right- 
hand  side  of  the  picture  about  thirty-five  feet  distant  from  E. 


We  can  see  only  half  of  the  Moon — namely,  that  half  that 
is  turned  toward  us.  An  eye  at  S  (on  the  left-hand  side 
of  the  page)  could  see  half  of  the  Moon  if  it  were  illumi- 
nated. But  as  the  dark  side  is  turned  toward  S  an  eye 
placed  there  would  see  nothing.  No  light  would  come  to 
it.  An  eye  at  V  would  see  the  Moon  as  a  bright  circle. 
The  half  turned  toward  V  is  fully  illuminated. 


218 


ASTRONOMY. 


In  this  figure  the  central  globe  is  the  Earth;  the  circle 
around  it  represents  the  orbit  of  the  Moon.  The  rays  of 
the  Sun  fall  on  both  Earth  and  Moon  from  the  right,  the 


FIG.  137.— THE  PHASES  OF  THE  MOON  EXPLAINED. 

Sun  being  some  thirty  feet  away  (on  the  scale  of  the  draw- 
ing) in  the  line  BA.  For  the  present  purpose  we  suppose 
both  Earth  and  Sun  to  be  at  rest  and  the  Moon  to  move 
round  her  orbit  in  the  direction  of  the  arrows.  Eight 
positions  of  the  Moon  are  shown  around  the  orbit  at  A,  E, 
<?,  etc.,  and  the  right-hand  hemisphere  of  the  Moon  is 
illuminated  in  each  position.  Outside  of  these  eight  posi- 
tions are  eight  pictures  showing  how  the  Moon  looks  as 
seen  from  the  Earth  in  each  position. 

At  A  it  is  "  new  Moon,"  the  Moon  being  nearly  between 
the  Earth  and   the   Sun.     Its  dark   hemisphere   is  then 


THE  MOTIONS  AND  PHASES  OF  THE  MOON.    219 

turned  towards  the  Earth,  so  that  it  is  entirely  invisible. 
The  Sun  and  Moon  then  rise  and  set  together.  They  are 
in  the  same  direction  in  space. 

At  E  the  observer  on  the  Earth  sees  about  a  fourth  of 
the  illuminated  hemisphere,  which  looks  like  a  crescent,  as 
shown  in  the  outside  figure.  In  this  position  a  great  deal 
of  light  is  reflected  from  the  Earth  to  the  Moon  and  back 
again  from  the  Moon  to  the  Earth,  so  that  the  part  of  the 
Moon's  face  not  illuminated  by  the  Sun  shines  with  a 
grayish  light.  At  C  the  Moon  is  in  her  first  quarter.  The 
Moon  is  on  the  meridian  about  G  P.M.  She  is  about  90° 
(6  hours)  east  of  the  Sun.  When  the  Sun  is  setting  the 
Moon  is  therefore  near  the  meridian.  At  G  three-fourths 
of  the  hemisphere  that  is  illuminated  by  the  Sun  is  visible 
to  the  observer;  and  at  B  the  whole  of  it  is  visible.  The 
Moon  at  B  is  exactly  opposite  to  the  Sun  and  it  is  then 
"full  Moon."  The  full  Moon  rises  at  sunset.  As  the 
Moon  moves  to  H,  D,  F,  the  phases  change  in  a  reverse 
order  to  those  of  the  first  half  of  the  month. 

The  Tides. — The  phenomena  of  the  tides  are  familiar  1o  those  who 
live  near  the  seashore.  Twice  a  day  the  waters  of  the  ocean  rise 
high  on  the  beach.  Twice  a  day  they  recede  outwards.  The  first 
"  high  tide  "  occurs  at  any  place  (speaking  generally)  about  the  time 
when  the  Moon  is  on  the  meridian  of  that  place.  About  six  hours 
later  comes  "low  tide";  about  twelve  hours  after  the  first  "high 
tide"  comes  a  second  "  hi^h  tide,"  and  finally,  about  six  hours  after 
this  a  second  "  low  tide."  The  Moon  revolves  about  the  Earth  once 
in  about  25h  (not  24h),  for  it  is  moving  eastwards  among  the  stars 
nearly  15°  daily. 

In  figure  138  suppose  0  to  be  the  centre  of  the  Earth  and  m  a 
place  on  its  surface.  Suppose,  for  simplicity,  that  the  whole  Earth 
is  surrounded  by  a  shallow  shell  of  water.  There  is  a  high  tide  at 
m  when  the  Moon  (M}  is  on  the  meridian  of  m.  Let  us  see  why  this 
is  so.  The  Earth  is  attracting  the  Moon,  and  by  its  attraction  the 
Moon  is  kept  in  her  orbit. 

The  Moon  moves  towards  the  Earth  a  little  every  second. 

The  Moon  likewise  attracts  every  particle  of  the  earth,  solid  and 
fluid  alike.  The  fluid  particles  nearest  M  (at  m)  are  perfectly  free 


220  ASTRONOMY. 

to  move,  and  they  are  therefore  heaj  ed  up  into  a  kind  of  a  wave 
whose  crest  is  at  ra.  The  particles  of  water  near  m'  and  m"'  are 
drawn  towards  m.  The  Moon  at  M  also  attracts  the  solid  body  of 


FIG.  138. — THE  TIDES  OF  THE  OCEAN  ARE  PRODUCED  BY  THE 
MOON'S  ATTRACTION. 

the  Earth  with  a  force  that  is  inversely  proportional  to  the  square  of 
the  distance  MO— to  —and  the  Earth  moves  towards  the  Moon 

a  little  every  second.  The  Moon  also  attracts  the  fluid  particles 
near  m',  in  the  further  hemisphere  of  the  Earth,  with  a  force  pro- 
portional to  If  they  were  a  solid  separate  from  the  main 

body  of  the  Earth,  they  would  move  less  than  the  rest  of  the  Earth, 
because  they  are  less  attracted,  being  more  distant. 

The  Moon  at  M  attracts  the  solid  Earth  as  a  whole,  more  than  it 
attracts  the  waters  of  the  distant  hemisphere  m"m'm'".  The  solid 
Earth,  which  must  move  as  a  whole,  moves  towards  M  in  consequence 
of  its  attraction  more  than  the  waters  of  the  distant  hemisphere, 
which  are  therefore  left  behind  as  it  were,  heaped  up  into  a  kind  of 
wave  whose  crest  is  at  m'  opposite  to  the  moon  M.  The  shape  of 
the  tidal  ellipsoid  is  shown  by  the  shaded  area  in  the  figure. 

When  the  moon  is  at  M  on  the  meridian  of  a  place  at  m,  the  tidal 
ellipsoid  is  as  drawn.  There  is  high  tide  at  m,  low  tide  at  a  place 
90°  distant  (m"),  high  tide  at  m',  low  tide  again  at  m'".  Whenever 


THE  MOTIONS  AND  PHASES  OF  THE  MOON.     221 

the  moon  is  on  the  meridian  ©f  any  place  such  an  ellipsoid  is  formed. 
As  the  Moon  moves  round  the  earth  each  day  from  rising  to  setting, 
this  ellipsoid  moves  with  it. 

In  an  hour  the  moon  will  have  moved  to  1'  and  the  crest  of  the 
wave  to  1.  The  tide  will  be  high  at  1  and  falling  at  ra.  As  the 
moon  moves  by  the  diurnal  motion  to  2',  3',  M"',  Mf,  the  crest  will 
move  with  it.  When  the  moon  is  at  M '"  it  is  low  water  at  m  and 
m'.  When  the  moon  is  at  M' ,  it  is  again  high  water  at  m  ;  and 
so  on. 

If  we  suppose  M  to  be  the  sun,  a  similar  set  of  solar  tides  will  be 
produced  every  24  hours.  The  actual  tide  is  produced  by  the  super- 
position of  the  solar  and  lunar  tides. 

The  foregoing  explanation  relates  to  an  Earth  covered  by  an  ocean 
of  uniform  depth.  To  fit  it  to  the  facts  as  they  are  a  thousand  cir- 
cumstances must  be  taken  into  account  which  depend  on  the  modify- 
ing effects  of  continents  and  islands,  of  deep  and  shallow  seas,  of 
currents  and  winds.  Practically  the  time  of  high  tide  at  any  station 
is  predicted  in  the  "  Tide-Tables"  by  adding  to  the  time  of  the 
Moon's  transit  over  the  meridian  a  quantity  that  is  determined  from 
observation  and  not  from  theory. 

—  Describe  the  changes  of  the  shape  of  the  Moon's  disk  from 
new  moon  to  the  next  new  moon.  Does  the  Moon  shine  by  her  own 
light?  What  part  of  the  globe  of  the  Moon  is  illuminated  by  the 
Sun  ?  About  what  time  does  the  new  moon  rise  ?  the  full  moon  ? 


CHAPTER   XII. 

ECLIPSES  OF  THE  SUN   AND  MOON 

27.  The  Earth's  Shadow — the  Moon's  Shadow — Lunar 
Eclipses — Solar  Eclipses — Occultations  of  Stars  by  the 
Moon. — A  point  of  light  L  sends  out  rays  in  every  direc- 
tion. If  an  opaque  disk  VO  is  interposed  in  the  path  of 
some  of  these  rays  it  will  form  a  shadow  on  the  side 
furthest  from  the  light.  All  the  space  between  the  lines 


FIG.  139. — THE  SHADOW  OF  A  DISK   VO  FORMED  BY  A  POINT  OP 
LIGHT  L  AND  PROJECTED  ON  A  SCREEN  T8. 

LV,  LO,  and  other  lines  drawn  from  the  point  L  to  the 
borders  of  VO  will  be  dark.  The  region  VOSTis  dark  and 
it  is  called  the  shadow  of  VO.  If  the  source  of  light  is 
not  a  mere  point  the  shadow  is  not  so  simple.  The  candle- 
flame  AB  shines  on  the  sphere  DC  and  illuminates  one- 
half  of  it.  The  region  to  the  right  of  the  sphere  and 
between  the  lines  BDS'  and  ACS  receives  no  light  at  all. 
If  a  screen  is  interposed  the  shadow  is  shown  quite  black 
at  S'S.  None  of  the  region  to  the  right  of  the  sphere 
between  the  lines  AP'  and  BP  is  fully  illuminated.  Some 
of  the  candle-flame  is  cut  off  from  every  part  of  this  region 


ECLIPSES  OF  THE  SUN  AND  MOON. 


223 


by  the  sphere.  Let  the  student  mark  a  point  half  way 
from  S  to  P  (call  it  a).  From  a  draw  a  line  tangent  to 
the  sphere  near  C  and  prolong  it  till  it  meets  the  candle- 


FIG.  140. — THE  SHADOW — UMBRA  AND  PENUMBRA— OP  A  SPHERE 
FOKMED  BY  A  CANDLE. 

flame  (at  a  point  that  we  may  call  b).  Draw  also  the  line 
a  A.  The  point  a  is  illuminated  by  part  of  the  flame  (.the 
part  between  I  and  A)  and  it  receives  no  light  from  the 
part  of  the  fl  me  between  b  and  B.  It  is  impossible  to 
draw  a  straight  line  through  a  that  will  meet  the  flame 
between  b  and  B  unless  such  a  line  passes  through  the 
sphere  DC.  The  region  DS'SC  is  the  umbra  of  the 
shadow;  the  region  DP' 8',  CSP,  etc.,  is  the  penumbra. 
If  the  shadow  is  received  on  a  screen  the  circle  SS'  is  often 
called  the  umbra  and  the  ring  PSP'S'  the  penumbra. 

The  Shadow  of  the  Earth.— In  figure  141  Sis  the  Sun, 
E  the  Earth.  The  cone  BVB'  is  the  umbra;  that  part  of 
the  cone  BPBT'  which  is  not  umbra  is  the  penumbra. 

Dimensions  of  the  Earth'' s  Stiadow.—'Let  us  investigate  the  distance 
EVfrom  the  centre  of  the  Earth  to  the  vertex  of  the  shadow.  The 
triangles  VEB  and  VSD  are  similar,  having  a  right  angle  at 
at  D,  Hence 

VE :  EB  =  VS :  SD  =  ES  :  (SD  -  EB). 


224: 


ASTRONOMY. 


So  if  we  put 

I  =  VE,  the  length  of  the  shadow   measured  from  the  centre  of 

the  Earth, 

r  =  ES,  the  radius-vector  of  the  Earth,  =  92,900,000  miles, 
R=  8D,  the  radius  of  the  Sun,  =       433,000      " 

p  =  EB  the  radius  of  the  Earth,  =  4000      "   , 

we  have 

E8  X  EB  _      rp 
.    SD-EB  ~  R  -  p 


FIG.  141. — DIMENSIONS  OF  THE  SHADOW  OP  THE  EARTH. 

That  is,  I  is  expressed  in  terms   of  known  quantities,  and  thus  is 
known. 
Its  length  is  about  866,000  miles. 


FIG.  142.— AB  is  THE  ECLIPTIC  ;  CD  is  THE  MOON'S  ORBIT. 

The  three  dark  circles  on  AB  are  three  positions  of  the  Earth's  shadow. 
Sometimes  the  Moon  is  totally  eclipsed  as  at  G,  sometimes  partially 
eclipsed  as  at  F,  sometimes  she  just  escapes  eclipse  as  at  E. 

Eclipses  of  the  Moon.— The  mean  distance  of  the  Moon 
from  the  Earth  is  about  238,000  miles  and  the  Moon  often 
passes  through  the  Earth's,  shadow-cone  (EV).  While, 


ECLIPSES  OF  THE  SUN  AND  MOON.  225 

the  Moon  is  within  that  cone  none  of  the  light  of  the  Sun 
can  reach  her  surface  and  she  is  said  to  be  eclipsed. 

If  the  Moon  moved  exactly  in  the  plane  of  the  ecliptic 
she  would  pass  through  the  Earth's  shadow-cone  at  every 
full  Moon  (for  it  is  at  full  Moon  that  the  Sun  and  Moon 
are  on  opposite  sides  of  the  Earth)  and  would  be  totally 
eclipsed  once  every  lunar  month.  The  Moon's  orbit  is, 
however,  inclined  to  the  ecliptic  at  an  angle  of  about  5°, 
and  therefore  she  often  escapes  eclipse,  as  is  shown  by  the 
diagram.  As  a  matter  of  fact  it  is  very  seldom  that  more 
than  two  lunar  eclipses  occur  in  any  calendar  year. 

Eclipses  of  the  Moon  are  calculated  beforehand  and  the  phases  are 
printed  in  the  almanac.  Supposing  the  Moon  to  be  moving  around 
the  Earth  from  below  upward  in  figure  141,  its  advancing  edge  first 
meets  the  boundary  B'P'  of  the  penumbra.  The  time  of  this  ocur- 
rence  is  given  in  the  almanac  as  that  of  Moon  entering  penumbra. 
A  small  portion  of  the  sunlight  is  then  cut  off  from  the  advancing 
edge  of  the  Moon,  and  this  amount  constantly  increases  until  the 
edge  reaches  the  boundary  B'  V  of  the  shadow.  The  eye  can 
scarcely  detect  any  diminution  in  the  brilliancy  of  the  Moon  until 
she  has  almost  touched  the  boundary  of  the  true  shadow.  The 
observer  must  not,  therefore,  expect  to  detect  the  corning  eclipse 
until  very  nearly  the  time  given  in  the  almanac  as  that  of  Moon 
entering  shadow.  As  the  Moon  enters  the  true  shadow  the  advancing 
portion  of  the  lunar  disk  will  be  entirely  lost  to  view.  It  takes  the 
Moon  about  an  hour  to  move  over  a  distance  equal  to  her  own  diam- 
eter, so  that  if  the  eclipse  is  nearly  central  the  whole  Moon  will  be 
immersed  in  the  shadow  about  an  hour  after  she  first  strikes  it. 
This  is  the  time  of  beginning  of  total  eclipse.  So  long  as  only  a 
moderate  portion  of  the  Moon's  disk  is  in  the  shadow,  that  portion 
will  be  entirely  invisible,  but  if  the  eclipse  becomes  total  the  whole 
disk  of  the  Moon  will  nearly  always  be  visible,  shining  with  a  red 
coppery  light. 

This  is  owing  to  the  refraction  of  the  Sun's  rays  by  the  lower 
strata  of  the  Earth's  atmosphere.  We  shall  see  hereafter  that  if  a 
ray  of  light  DB  (see  Fig.  141)  passes  from  the  Sun  to  the  Earth,  so 
as  just  to  graze  the  latter,  it  is  bent  by  refraction  more  than  a  degree 
out  of  its  course.  At  the  distance  of  the  Moon  the  whole  shadow  of 
the  Earth  is  filled  with  this  refracted  light.  Some  of  it  is  reflected 
back  to  the  Earth,  and  as  it  has  passed  twice  through  the  Earth's 


226  ASTRONOMY. 

atmosphere  the  light  is  red  for  the  same  reason  that  the  light  of  the 
setting  Sun  is  red. 

The  Moon  may  remain  enveloped  in  the  shadow  of  the  Earth 
during  a  period  ranging  from  a  few  minutes  to  nearly  two  hours, 
according  to  the  distance  at  which  she  passes  from  the  axis  of  the 
shadow  and  the  velocity  of  her  angular  motion.  When  she  leaves 
the  shadow,  the  phases  which  we  have  described  occur  in  reverse 
order. 

It  very  often  happens  that  the  Moon  passes  through  the  penumbra 
of  the  Earth's  shadow  without  touching  the  shadow  at  all.  The 
diminution  of  light  in  such  cases  is  scarcely  perceptible  unless  the 
Moon  at  least  grazes  the  edge  of  the  shadow. 

Eclipses  of  the  Sun. — The  shadow  of  the  Earth  falling 
upon  the  Moon  cuts  off  the  Sun's  light  from  it  and  causes 
a  lunar  eclipse.  The  shadow  of  the  Moon  falling  on  a  part 
of  the  Earth  cuts  off  the  light  of  the  Sun  from  all  observers 
in  that  region  of  the  Earth  and  causes  a  solar  eclipse. 


FIG.  143.— DIMENSIONS  OF  THE  SHADOW  OF  THE  MOON. 

In  this  figure  let  8  represent  the  Sun,  as  before,  and  let 
E  represent  the  Moon.  The  cone  B  VB'  is  now  the  umbra 
of  the  Moon's  shadow.  We  wish  to  know  the  length  of 
ths  Moon's  shadow  VE.  By  a  method  similar  to  that 
given  on  page  224,  using  accurate  values  of  the  different 
quantities,  it  is  found  that  VE  at  new  Moon  is  about 
232,000  miles.  The  average  distance  of  the  centre  of  the 
Moon  from  the  centre  of  the  Earth  is  about  239,000  miles 
(or  from  the  centre  of  the  Moon  to  the  surface  of  the  Earth 


ECLIPSES  OF  TEE  SUN  AND  MOON.  227 

abont  235,000  miles),  and  hence  generally  the  Moon's 
shadow  will  not  quite  reach  to  the  Earth's  surface  and 
generally  there  will  be  no  solar  eclipse  at  new  Moon.  If 
the  Moon's  orbit  were  a  circle  with  a  radius  of  239,000 
miles  we  should  have  no  solar  eclipses  at  all.  It  is,  how- 
ever, an  ellipse,  and  at  favorable  times  (that  is  when  the 
Moon's  shadow  is  long  enough  and  when  it  points  at  the 
Earth)  the  Moon's  shadow  may  reach  the  Earth  and  even 
beyond  it.  At  such  times  the  Sun's  light  will  be  cut  off 
from  all  observers  on  the  Earth  within  the  shadow  and  a 
solar  eclipse  will  occur.  The  conditions  at  such  favorable 
times  are  illustrated  by  the  figure. 


FIG.  144. 

The  Sun  is  eclipsed  to  all  observers  on  the  Earth  within  the  shadow  of 
the  new  moon  (A).  The  full  Moon  is  eclipsed  whenever  it  passes  through 
the  Earth's  shadow  (B). 

It  is  clear  that  all  observers  on  the  Earth  within  the 
umbra  of  the  Moon's  shadow  at  A  cannot  see  the  Sun  at 
all.  To  them  the  Sun  will  be  totally  eclipsed.  Observers 
on  the  Earth  within  the  penumbra  of  the  Moon's  shadow 
(see  the  figure)  will  see  a  part  of  the  Sun  only.  To  such 
observers  the  Sun  will  be  partially  eclipsed. 

The  diameter  of  the  Moon's  umbra  at  the  surface  of  the 
Earth  is  seldom  more  than  160  miles.  It  is  usually  much 
less.  Observers  within  this  umbra  see  a  total  solar  eclipse. 
As  the  Moon  moves  in  its  orbit  at  the  rate  of  over  2000 
miles  per  hour  (which  is  about  twice  the  velocity  of  a 
cannon-ball)  the  shadow  moves  correspondingly.  It  sweeps 


228  ASTRONOMY. 

over  the  surface  of  the  Earth  in  a  curved  line  or  belt.  The 
observers  within  this  belt  see  the  total  eclipse  one  after 
another.  At  any  one  place  the  totality  cannot  last  more 
than  8  minutes  and  it  usually  lasts  much  less  than  this. 

At  the  total  solar  eclipse  of  July,  1878,  for  example,  the  shadow  of 
the  Moon  travelled  diagonally  across  North  America  from  Behring's 
Straits  through  Alaska  west  of  the  Rocky  Mountains  of  British  Co- 
lumbia and  entered  the  United  States  not  far  east  of  Vancouver. 
From  thence  the  shadow  crossed  Washington,  Idaho,  the  south- 
western part  of  Wyoming,  the  State  of  Colorado  (near  Denver),  the 
State  of  Texas,  and,  curving  across  the  Gulf  of  Mexico,  traversed 
Cuba.  The  duration  of  totality  was  about  3  minutes  near  Van- 
couver, about  2|  minutes  near  Galveston.  The  shadow-path  of  the 
total  solar  eclipse  of  May  28,  1900,  is  described  in  Chapter  XVI. 

In  order  to  see  a  total  eclipse  an  observer  must  station 
himself  beforehand  at  some  point  of  the  Earth's  surface 
over  which  the  shadow  is  to  pass.  These  points  are  gen- 
erally calculated  some  years  in  advance,  in  the  astronomical 
ephemerides. 

Eclipses  of  the  Sun  are  useful  to  astronomy  because 
during  an  eclipse  the  Sun's  light  is  cut  off  from  the  Earth's 
atmosphere  and  we  have  a  short  period  of  darkness  during 
which  the  surroundings  of  the  San  can  be  examined  with 
the  spectroscope  or  with  the  photographic  camera.  Great 
discoveries  have  been  made  at  these  times,  as  we  shall  see. 
Eclipses  are  useful  to  history  and  to  chronology  because  they 
afford  a  precise  means  of  fixing  dates.  Total  solar  eclipses 
are  so  impressive  (see  Chapter  XVI  for  a  description  of  the 
phenomena)  that  they  are  often  recorded  in  ancient  annals. 
Calculation  can  fix  the  date  at  which  such  an  event  was 
visible,  and  thus  render  a  service  to  chronology.  Lunar 
eclipses  are  often  serviceable  in  the  same  way. 

There  is  another  way  of  looking  at  the  problem  of  solar 
eclipses  which  is  worth  attention.  An  observer  on  the 
Earth  sees  the  Sun  as  a  bright  circle  in  the  sky.  The 
apparent  angular  diameter  of  the  Sun  (the  angle  between 


ECLIPSES  OF  TEE  SUN  AND  MOON. 


229 


two  lines  drawn  from  the  observer's  eye  to  the  upper  edge 
and  to  the  lower  edge  of  the  San,  respectively)  is  greatest 
when  the  Earth  is  nearest  to  the  Sun,  least  when  the  Earth 
is  farthest  away.  In  the  same  way  the  apparent  angular 
diameter  of  the  Moon  to  an  observer  on  the  Earth  is 
greatest  when  the  Moon  is  nearest,  least  when  the  Moon  is 
furthest  away. 

These  apparent  angular  diameters  have  been  measured 
and  the  results  of  observation  are  given  in  the  following 
little  table: 


Greatest. 

Least. 

Average. 

Apparent  diameters  of  the  Moon  ... 
Apparent  diameters  of  the  Sun  

33'  33" 
32'  33" 

29  24" 

31'  28" 

31'  08" 
32'  00" 

If  at  any  new  Moon  the  centres  of  the  Sun,  Moon,  and 
Earth  are  in  a  straight  line,  an  eclipse  will  occur.     If  the 


C 


FIG.  115. 

angular  diameter  of  the  Moon  is  less  than  that  of  the  Sun 
we  shall  have  an  annular  eclipse  of  the  Sun.  When  the 
centre  of  the  Moon  just  covers  the  centre  of  the  Sun  the 
appearance  will  be  like  figure  146.  As  the  Sun  at  this  time 
has  a  larger  angular  diameter  it  will  appear,  at  the  moment 
of  central  eclipse,  like  a  bright  ring  round  the  dark 
(unilluminated)  body  of  the  Moon.  The  Moon  will  move 
across  the  disk  of  the  Sun  from  west  towards  east  and  the 
ring  will  only  endure  for  a  short  time. 

If  the  centres  of  the  Earth,  Sun,  and  Moon  are  in  a 
straight  line  at  any  new  Moon,  and  if  at  that  time  the 
apparent  angular  diameter  of  the  Moon  is  greater  than  that 
of  the  Sun  there  will  be  a  total  eclipse  of  the  Sun. 


230 


ASTRONOMY. 


If  at  the  time  of  new  Moon  the  Moon  does  not  pass 
centrally  across  the  Sun's  disk,  but  above  the  centre  or 
below  it,  there  may  be  a  total  eclipse  (or  an  annular  eclipse), 
but  usually  there  will  only  be  a  partial  eclipse.  Only  a 
part  of  the  Sun's  disk  will  be  covered  in  such  a  case. 

There  are  more  eclipses  of  the  Sun  than  of  the  Moon. 
A  year  never  passes  without  at  least  two  of  the  former,  and 
sometimes  five  or  six,  while  there  are  rarely  more  than  two 
eclipses  of  the  Moon,  and  in  many  years  none  at  all.  But 
at  any  one  place  on  the  Earth  more  eclipses  of  the  Moon 
than  of  the  Sun  will  be  seen.  The  reason  of  this  is  that  an 

eclipse  of  the  Moon  is 
visible  over  the  entire 
hemisphere  of  the  Earth 
on  which  the  Moon  is 
shining,  and  as  it  lasts 
several  hours,  observers 
who  are  not  in  this  hemis- 
phere at  the  beginning  of 
the  eclipse  may,  by  the 
Earth's  rotation,  be 
brought  into  it  before  it 
ends.  Thus  the  eclipse 
FIG.  146.— Tms  DARK  BODY  OF  wm  nsually  be  seen  over 
THE  MOON  PROJECTED  ON  THE  ,.  ;  .,  ,.  ,.,  ,.  , 

DISK  OF  THE  SUN  AT  THE  MID-  more  than  half  the  Earth's 
DLE  OF  AN  ANNULAR  ECLIPSE,  surface.  But  each  eclipse 
of  the  Sun  can  be  seen  over  only  so  small  a  part  of  the 
Earth's  surface,  and  while  there  are  many  more  solar 
eclipses  than  lunar  for  the  whole  Earth  taken  together, 
fewer  are  visible  at  any  one  station. 

Occultation  of  Stars  by  the  Moon.— Since  all  the  bodies  of  the  solar 
system  are  nearer  than  the  fixed  stars,  it  is  evident  that  they  must 
from  time  to  time  pass  between  us  and  the  stars.  The  planets  are, 
however,  so  small  that  such  a  passage  is  of  very  rare  occurrence. 
But  the  Moon  is  so  large  and  her  angular  motion  so  rapid  that  she 


ECLIPSES  OF  THE  SUN  AND  MOON.  231 

passes  over  some  star  visible  to  the  naked  eye  every  few  days. 
Such  phenomena  are  termed  occultations  of  stars  by  the  Moon. 

The  Nautical  Almanac  contains  predictions  of  all  occultations, 
These  predictions  are  obtained  by  calculating  the  Moon's  path  on 
the  celestial  sphere  and  by  noticing  what  bright  stars  (or  planets) 
her  disk  will  cover  to  observers  at  different  stations  on  the  Earth. 

—  What  is  a  shadow  ?  its  umbra  ?  penumbra  ?  Draw  a  diagram 
showing  the  shadow  of  the  Earth  cast  by  the  Sun.  Point  out  the 
umbra  and  the  penumbra  of  this  shadow.  What  is  the  cause  of  a 
lunar  eclipse?  Why  do  we  not  have  lunar  eclipses  at  every  full 
moon — once  a  month  ?  What  is  the  color  of  the  totally  eclipsed 
moon  ?  Why  does  it  have  this  color  ?  What  is  the  cause  of  a  solar 
eclipse  ?  Why  do  we  not  have  solar  eclipses  at  every  new  moon  ? 
(Answer:  because  in  the  first  place  the  Moon's  shadow  is  often  too 
short  to  reach  the  surface  of  the  Earth  and  also  because  it  often 
does  not  at  new  Moon  point  at  the  Earth,  but  above  the  Earth  or 
below  it.) 


FIG.  147. — A  SCHOOLROOM  EXPERIMENT  TO  ILLUSTRATE  A 

SOLAR  ECLIPSE. 

The  room  must  be  darkened.  The  lamp  should  have  a  ground  glass  or 
an  opal  globe  to  represent  the  circle  of  the  Sun's  disk.  An  orange  (B) 
fastened  to  a  pincushion  by  a  knitting-needle  may  stand  for  the  Earth. 
A  golf -ball  suspended  by  a  string  (C)  may  stand  for  the  Moon.  By  placing 
C  on  the  other  side  of  B  the  circumstances  of  a  lunar  eclipse  may  be  illus- 
trated. 

What  is  a  partial  eclipse  of  the  Moon  ?  of  the  Sun  ?  a  total 
eclipse  of  the  Moon?  of  the  Sun?  an  annul-ir  eclipse  of  the  Sun? 
Why  can  there  never  be  an  annular  eclipse  of  the  Moon  ?  What  is 
an  occultation  f  LONGFELLOW  has  a  poem,  "  The  Occultation  of 
Orion."  Could  the  Moon  cover  a  whole  constellation  ? 


CHAPTER   XIII. 
THE  EARTH. 

28.  Astronomy  has  to  do  with  the  Earth  as  a  planet. 
Physical  Geography  treats  of  the  Earth  without  considering 
its  relation  to  the  other  bodies  of  the  solar  system.  But 
our  only  means  of  understanding  the  conditions  on  other 
planets  is  to  be  found  in  a  comparison  of  these  conditions 
with  circumstances  on  the  Earth.  For  this  reason  it  is 
convenient  to  recall  some  of  the  facts  taught  by  Physical 
Geography  and  to  group  them  with  others  derived  from 
Astronomy. 

The  Earth's  average  distance  from  the  Sun  is  about  92,800,000 
miles.  Its  least  distance  (in  December)  is  91,250,000  miles;  its 
greatest  distance  (in  June)  is  94,500,000  miles.  The  seasons  on  the 
Earth  depend  chiefly  on  the  north-polar  distance  of  the  Sun  and  not 
on  the  Earth's  proximity  to  it.  The  Earth  revolves  on  its  axis  once 
in  24  (sidereal)  hours.  By  its  rotation  an  observer  at  the  equator  is 
carried  round  at  the  rate  of  more  than  1000  miles  per  hour.  It  was 
a  favorite  argument  of  the  men  of  the  Middle  Ages  against  the 
theory  that  the  earth  was  in  rotation  that  so  great  a  velocity  as  this 
could  not  possibly  fail  to  be  remarked.  If  the  rotation  were  not 
uniform  and  regular  the  argument  would  be  convincing. 

The  Earth  travels  around  the  circumference  of  its  orbit  once  in 
365  days,  at  the  rate  of  about  66,000  miles  per  hour,  at  the  rate  of 
about  18j  miles  per  second. 

Figure  of  the  Earth. — PTOLEMY  taught  in  the  Almagest 
(A.D.  140)  that  the  Earth  was  a  sphere.  Five  hundred 
years  before  his  time  ARISTOTLE  had  proved  the  same 
thing,  and  before  ARISTOTLE  there  were  philosophers  who 
held  the  same  opinion.  PTOLEMY  maintained  that  the 


THE  EARTH.  233 

Earth  was  rounded  in  an  east-to-west  direction  because  the 
Sun,  Moon,  and  stars  do  not  rise  and  set  at  the  same 
moment  to  all  observers,  but  at  different  moments.  The 
Earth  was  rounded  in  a  north  and  south  direction  because 
new  stars  appeared  above  the  southern  horizon  as  men 
travelled  southwards,  or  above  the  northern  horizon  as  they 
travelled  northwards. 

It  was  well  known  in  his  time  that  a  journey  of  a  few 
hundred  miles  to  the  north  or  south  would  change  the 
horizon  of  an  ol server  so  that  new  stars  became  visible. 
Such  short  journeys  could  not  produce  such  results  on  a 
globe  of  very  large  size.  The  voyage  of  MAGELLAN  at  the 
'  beginning  of  the  sixteenth  century  first  established  in  all 
men's  minds  the  fact  that  the  Earth  was  a  spherical  body. 


FIG.  148.— AN  ELLIPSE. 
AC  =  2a  is  the  major  axis ;  BD  =  2b  is  the  minor  axis 

The  popular  opinion  for  many  centuries  was  that  the  Earth 
was  a  flat  disk  everywhere  surrounded  by  water. 

The  Earth  is  not  a  sphere,  but  a  spheroid.  If  it  is  cut 
by  meridian  planes  (through  the  poles)  the  curves  cut  out 
of  its  surface  are  ellipses,  not  circles. 


234: 


ASTRONOMY. 


If  an  ellipse  is  revolved  about  the  axis  BD  the  resulting 
solid  is  a  spheroid.  The  Earth's  meridian  is  very  little 
different  from  a  circle.  The  minor  axis,  the  line  joining 
the  two  poles,  is  the  axis  of  rotation. 


NO 


FIG.  149.— THE  EARTH— ITS  Axis,  ITS  POLES,  ITS  EQUATOR. 

Its  equatorial  semi-diameter   =  a  =  20,926,202  feet, 

-  3963.296  miles, 
=  6,378,190  metres. 


Its  polar  semi-diameter 


The  equatorial  diameter 
"    polar  " 


=  6  =  20,854.895  feet, 
=  3949.790  miles, 
=  6,356,456  metres. 

=  2a  =  7926  6  miles, 
=  2b  =  7899.6     " 

=  about  500,000,000  inches. 


The  circumference  of  the  equator  =  24.899  miles, 
*'  "  "  a  meridian    =24,856     " 

=  40,000,000  metres. 

A  railway  train  travelling  a  mile  a  minute  would  require  17  days 
and  nights  of  continuous  travel  to  go  once  around  the  Earth. 
The  area  of  the  whole  Earth  is  about  197,000,000  square  miles. 
«       "     «     «   dryland          "      "       50,000,000       "         "    . 


THE  EARTH.  235 

So  that  the  area  of  the  Earth  is  more  than  fifty  times  that  of  the 
United  States.  We  shall  see  that  the  planets  Jupiter,  Saturn, 
Uranus,  and  Neptune  are,  each  one  of  them,  far  larger  than  the 
Earth  ;  and  the  Sun  is  immensely  larger.  Its  diameter  is  866,400 
miles. 

Geodetic  Surveys. — Since  it  is  practically  impossible  to 
measure  around  or  through  the  Earth,  the  figure  and  the 
size  of  our  planet  has  to  be  found  by  combining  measure- 
ments on  its  surface  with  astronomical  observations.  Even 
a  measurement  on  the  Earth's  surface  made  in  the  usual 
way  of  surveyors  would  be  impracticable,  owing  to  the  in 
tervention  of  mountains,  rivers,  forests,  and  other  natural 
obstacles.  The  method  of  triangulation  is  therefore  uni- 
versally adopted  for  measurements  extending  over  large 
areas. 


FIG.  150.— A  PART  OF  THE  FRENCH  TRIANGULATION  NEAR  PARIS. 

Triangulation  is  executed  in  the  following  way:  Two  points,  a  and 
6,  a  few  miles  apart,  are  selected  as  the  extremities  of  a  base-line. 
They  must  be  so  chosen  that  their  distance  apart  can  be  accurately 
measured;  the  intervening  ground  should  therefore  be  as  level  and 
free  from  obstruction  as  possible.  One  or  more  elevated  points,  EF, 
etc.,  must  be  visible  from  one  or  both  ends  of  the  base-line.  The 
directions  of  these  points  relative  to  the  meridian  are  accurately 
observed  from  each  end  of  the  base,  as  is  also  the  direction  ab  of  the 
base-line  itself.  Suppose  Fto  be  a  point  visible  from  each  end  of 
the  base,  then  in  the  triangle  abF  we  have  the  length  ab  determined 


236  ASTRONOMY. 

by  actual  measurement,  and  the  angles  at  a  and  b  determined  by 
observations.  With  these  data  the  lengths  of  the  sides  aF  and  bF 
are  determined  by  a  simple  computation. 

The  observer  then  transports  his  instruments  to  F,  and  determines 
in  succession  the  direction  of  the  elevated  points  or  hills  DEOHJ, 
etc.  He  next  goes  in  succession  to  each  of  these  hills,  and  deter- 
mines the  direction  of  all  the  others  which  are  visible  from  it. 
Thus  a  network  of  triangles  is  formed,  of  which  all  the  angles  are 
observed,  while  the  sides  are  successively  calculated  from  the  first 
base.  For  instance,  we  have  just  shown  how  the  side  aFis  calcu- 
lated; this  forms  a  base  for  the  triangle  EFa,  the  two  remaining 
sides  of  which  are  computed.  The  side  EF  forms  the  base  of  the 
triangle  OEF,  the  sides  of  which  are  calculated,  etc. 

Chains  of  triangles  have  thus  been  measured  in  Russia  and  Sweden 
from  the  Danube  to  the  Arctic  Ocean,  in  England  and  France  from 
the  Hebrides  to  the  Sahara,  in  this  country  down  nearly  our  entire 
Atlantic  coast  and  along  the  great  lakes,  and  through  shorter  dis- 
tances in  many  other  countries.  An  east  and  west  line  has  been 
measured  by  the  Coast  Survey  from  the  Atlantic  to  the  Pacific 
Ocean. 

Suppose  that  we  take  two  stations,  a  and  j,  Fig.  150,  situated  north 
and  south  of  each  other,  determine  the  latitude  of  each,  and  calcu- 
late the  distance  between  them  by  means  of  triangles,  as  in  the 
figure.  It  is  evident  that  by  dividing  the  distance  between  them  by 
the  difference  of  latitude  in  degrees  we  shall  have  the  length  of  one 
degree  of  latitude.  Then  if  the  Earth  were  a  sphere,  we  should  at 
once  have  its  circumference  by  multiplying  the  length  of  one  degree 
by  360.  It  is  thus  found  that  the  length  of  1  degree  is  a  little  more 
than  111  kilometres,  or  between  69  and  70  English  statute  miles.  Its 
circumference  is  therefore  about  40,000  kilometres,  and  its  diameter 
between  12,000  and  13,000.*  (25,000  and  8000  miles.) 

The  general  surface  of  the  Earth  is  found  to  be  rather  smooth. 
The  highest  mountain  is  about  5£  miles  high;  the  deepest  ocean  is 
about  5£  miles  deep.  Eleven  miles  covers  the  range  of  height  and 
depth.  The  average  elevation  of  the  continents  above  the  sea-level 
is  about  2000  feet.  The  average  depth  of  the  ocean  is  about 
12,000  feet. 

*  When  the  metric  system  was  originally  designed  by  the  French,  it  was  in- 
tended that  the  kilometre  should  be  mJun  of  the  distance  from  the  pole  of  the 
Earth  to  the  equator.  This  would  make  a  degree  of  the  meridian  equal,  on  the 
average,  to  111$  kilometres.  But  the  metre  actually  adopted  is  nearly  Tjn  of  an 
inch  too  short. 


TEE  EARTH.  237 


MASS  AND  DENSITY  OF  THE  EARTH. 

The  mass  of  a  body  is  the  quantity  of  matter  it  contains.     It  is 
measured  by  the  product  of  its  volume  (  V)  by  its  density  (D) 

M  =  V  .  D.     For  another  body    M  '=  V'\  D'. 
For  equal  volumes     V  =  V     and    M:M'  =  D:D'. 

That  is,  the  densities  of  equal  volumes  of  two  substances  are  pro- 
portional to  the  masses  of  the  substances,  to  the  quantity  of  matter 
in  them.  For  example,  copper  is  of  greater  density  than  water 
because  a  cubic  foot  of  copper  contains  more  matter  than  a  cubic 
foot  of  water.  The  density  of  pure  water  at  about  39°  Fahr.  is 
taken  as  the  unit-density.  The  unit-volume  may  be  taken  as  a 
cubic  foot.  The  unit-mass  will  then  be  that  of  a  cubic  foot  of  pure 
water  at  39°  Fahr. 

The  weight  of  a  body  is  the  force  with  which  it  is  attracted  to  the 
centre  of  the  Earth.     A  body  of  mass  m  is  attracted  by  the  Earth's 
Mm 
r* 

weight  w  of  m  is  then  —  y-  .     The  weight  w'  of  any  other  body  m' 

is  w'=  —  jf  .     If  the  bodies  are  at  the  same  place  on  the  Earth  r  =  r1 

and  w  :  w'  =  m  :  m',  or  the  weights  of  bodies  at  the  same  place  on  the 
Earth  are  proportional  to  their  masses.  It  is  easy  to  measure  the 
relative  weights  of  two  bodies  by  balancing  them  in  scales  against 
certain  pieces  of  metal.  Hence  by  weighing  two  bodies  of  weights 
w  and  w'  we  can  determine  the  ratio  of  their  masses  m  and  m'.  If 
m  is  a  cubic  foot  of  water,  m'  is  the  absolute  mass  of  the  other 
substance. 

The  weight  of  a  body  m  due  to  the  Earth's  attraction  is 


.     If  the  body  is  at  the  pole  of  the  Earth  r  =  7899.6 

miles.  If  it  is  at  the  equator  r  =  7926.6  miles.  Its 
weight  will  therefore  be  greater  at  the  pole  than  at  the 
equator.  If  we  wish  to  weigh  out  a  certain  quantity  of 
gunpowder  in  Greenland  we  may  balance  it  against  a  piece 
of  metal  that  we  call  an  ounce.  If  we  take  the  gunpowder 
to  Peru  it  will  "weigh"  less  because  it  will  there  be 


238  ASTRONOMY. 

further  from  the  Earth's  centre.  Bat  it  will  still  balance 
the  ounce  in  Pern,  because  that  also  is  less  attracted  by  the 
Earth  in  precisely  the  same  proportion.  A  piece  of  iron  a 
cubic  foot  in  volume  "  weighs"  less  in  a  balloon  than  at 
the  Earth's  surface.  In  practical  life  no  note  need  be 
taken  of  the  differences  of  the  Earth's  attraction  at  differ- 
ent latitudes.  But  in  Astronomy  these  differences  of  at- 
traction due  to  differences  of  distance  must  be  taken  into 
account.  The  attraction  of  the  Earth  for  the  Moon  is 
different  at  different  times  because  the  Moon  is  sometimes 
near  the  Earth,  sometimes  further  away. 

The  density  of  pure  water  at  about  39°  Fahr.  is  taken  as  the  unit- 
density.  For  equal  volumes  of  any  two  substances  M :  M'  =  D  :  D' 
or,  their  densities  are  proportional  to  their  masses.  At  the  same 
place  on  the  Earth  W :  W  =  M :  M'  or,  their  weights  are  also  pro- 
portional to  their  masses,  hence 

W:W'=  D:  D'. 

If  one  of  these   substances   is  pure   water  (W,   D')  we  have 

W  D' 

D  =        '  ,      and  we  can  determine  D,  the  density  of  any  substance, 

as  copper,  by  weighing  it  against  an  equal  volume  of  water.  In 
this  way  the  densities  of  all  substances  on  the  Earth  have  been 
determined. 

The  surface-rocks  of  the  Earth  are  about  2£  times  as  dense  as 
water,  and  volcanic  lavas  deep  down  in  the  Earth  are  about  3  times 
as  dense.  The  deeper  the  origin  of  the  rocks  the  denser  they  are, 
because  they  are  subject  to  greater  pressures.  We  can  determine 
the  density  of  any  single  specimen  of  rock  that  can  be  brought  to 
the  surface.  We  can  get  no  specimens  of  rock  from  depths  greater 
than  a  few  miles.  How  then  shall  we  determine  the  average  density 
of  the  whole  Earth  ? 

To  determine  the  density  of  the  Earth  we  must  find  how  much  matter 
it  must  contain  in  order  to  attract  bodies  on  its  surface  with  forces 
equal  to  their  observed  weights,  that  is,  with  such  intensity  that  at  the 
equator  a  body  sJiallfall  nearly  fine  metres  (about  Wfeet)  in  a  second. 
To  find  this  we  must  know  the  relation  between  the  mass  of  a  body  and 
its  attractive  force.  This  relation  can  be  found  by  measuring  the 
attraction  of  a  body  of  known  mass. 


THE  EARTH.  239 

We  may  measure  the  attraction  of  a  body  of  known  mass  in  the 
following  ingenious  way.  In  Fig.  151  H1KL  is  a  cube  of  lead  1  metre 
on  each  edge.  Two  holes  are  bored 
through  the  cube  at  DF  and  EG- 
A  pair  of  scales  ABC  bas  its  scale- 
pans  DE  connected  by  fine  wires 
to  other  scale-pans  FG,  below  the 
block.  Suppose  the  pans  empty 
and  everything  at  rest. 

I.  Put  a  weight   W  in  D,   and 
balance  the  scales  by  weights  in  G, 
At  D  the  total  attraction  on  W  is 

the  attraction  of  the  Earth  plus  the  FIG.     151    —  EXPERIMENT    TO 

attraction  of  the   block,    while  at       DETERMINE  THE  DENSITY  OP 

G  we   have  the   attraction  of  the       THE  EAKTH- 

Earth  (downwards)  minus  the  attraction  of  the  block  (upwards); 

hence 

The  weight  in  D  4-  (attraction  of  the  block)  =  The  weights  in  G  — 
(attraction  of  the  block),  whence 

(1)  Weights  in  G  —  weight  in  D  +  2  (attraction  of  block). 

II.  Put  the  weight  W  in  F,  and  balance  the  scales  by  weights  in 
E.     At  F  the  total  attraction  is  earth  minus  block,  and  at  E  it  is 
earth  plus  block. 

The  weight  in  F  —  (attraction  of  the  block)  =  The  weights  in  E  -f- 
(attraction  of  the  block),  whence 

(2)  Weights  in  E  -  weight  in  F  -  2  (attraction  of  block). 

Subtract  equation  (2)  from  (1),  remembering  that  the  (weight  in 
D)  =  (weight  in  F). 

Weights  in  G  —  weights  in  E  =  4  (attraction  of  block), 

after  small  corrections  have  been  applied  for  the  difference  of  height 
of  D,  E,  F,  G,  etc. 

The  attraction  of  this  block,  which  has  a  known  mass  in  kilo- 
grammes (or  pounds),  is  thus  known,  and  hence  the  general  relation 
between  mass  in  kilogrammes  (or  pounds)  and  attractions. 

The  attraction  of  the  Earth  is  known.  It  is  such  as  to  cause 
bodies  to  have  their  observed  weights.  Hence  the  mass  of  the  Earth 
becomes  known.  The  volume  of  the  Earth  is  known  from  geodetic 


240 


ASTRONOMY. 


surveys.     The  density  of  the  whole  Earth  is  therefore  known  from 
the  equation  D  =  -=  . 

The  density  of  the  Earth  is  about  5£  times  that  of  water, 
"        "        "  copper        "      "     8£     "        "     "      "     , 


The  mass  of  the  Earth  is  6,000,000,000,000,000,000,000  tons. 


FIG.  152. 

Determination  of  the  Mass  of  the  Earth  in  Terms  of  the  Mass  of  the 
Sun. — The  mass  of  the  Earth  expressed  in  tons  or  pounds  is  known 
The  mass  of  the  Earth  in  fractions  of  the  Sun's  mass  (=  1.0)  can  be 
determined  by  calculating  how  far  the  Earth  is  deflected  by  the  Sun's 
attraction  each  second,  as  she  travels  in  her  orbit.  Her  motion 
along  her  orbit  is  18£  miles  per  second  (because  the  circumference  of 
her  orbit  is  584,600,000  miles  and  because  it  is  traversed  in  a  sidereal 
year  of  365d  9h  9m  9s).  (Fig.  152.)  Her  deflection  from  a  straight 
line  each  second  is  y1^  of  an  inch,  as  may  be  proved  from  the 
foregoing  diagram,  in  which  E  is  the  place  of  the  Earth  at  the 
beginning  of  a  second,  E'  its  place  at  the  end  of  the  second,  EE'  the 
orbit  of  the  Earth,  8  the  place  of  the  Sun,  X  another  point  of  the 
Earth's  orbit,  Ee  the  Earth's  fall  towards  the  Sun  in  a  second. 

In  the  two  right  triangles  XE'E  and  EE'e  we  have  EX  :  EE' 
=  EE' :  Ee,  or  (twice  93,000,000) :  18|  =  181  '•  Ee>  whence  Ee  =  0.01 
of  a  foot,  approximately. 

The  mass  of  the  Sun  at  93,000,000  miles  causes  the  Earth  to  move 
towards  his  centre  0.01  foot.  If  the  Sun  were  4000  miles  from 
the  Earth  his  attraction  would  be  greater  in  the  proportion  of 
[93,000,000]'  to  [4000]2  or  as  8,650,000,000,000,000  to  16,000,000  or 
as  540,500,000  to  1.  If  the  Sun  were  at  a  distance  of  only  4000  miles 
from  the  Earth  (or  from  any  heavy  body)  the  body  would  fall  in  a 
second  540,500,000  times  T^  of  a  foot  or  5,405,000  feet.  The  Earth 


THE  EARTH.  241 

makes  a  heavy  body  at  its  surface  (4000  miles  from  its  centre)  fall 
IGyV  feet  in  a  second.  Hence 

Mass  of  Sun  :  Mass  of  Earth  =  5,405,000  feet :  16.1  feet, 

or  as  335,000  to  1.  If  the  exact  values  of  all  the  quantities  are 
employed  instead  of  the  approximate  ones  used  above  the  value  of 
the  Earth's  Mass  (Sun's  Mass  =  1.0)  is  aygVnF- 

Constitution  of  the  Earth.— The  body  of  the  Earth  is 
made  up  of  layers  of  rocks  of  different  density  arranged  in 
shells  like  the  coats  of  an  onion.  The  outer  layers  are  the 
least  dense;  the  inner  layers  (those  subject  to  the  greatest 
pressures)  are  the  most  dense.  The  Earth  is  composed  of 
various  substances,  some  simple  (elements)  like  iron,  some 
compound  like  clay.  There  are  about  70  or  80  elementary 
^substances  (gold,  iron,  carbon,  oxygen,  hydrogen,  etc.),  and 
v  it  is  noteworthy  that  nearly  all  of  these  elements  are  known 
to  exist  in  the  Sun,  and  that  many  of  them  are  known  to 
exist  in  the  stars.  It  is  probable  that  the  Sun,  the  Earth, 
and  all  the  planets  are  made  out  of  the  same  elements  and 
that  the  amazing  differences  between  them  are  chiefly  due 
to  differences  in  their  temperature. 

The  temperature  of  the  solid  crust  of  the  Earth  increases  as  we  go 
downwards  at  the  rate  of  about  1°  Fahr.  for  every  55  or  60  feet,  or 
about  90°  per  mile.  At  the  depth  of  10  miles  the  temperature  is 
about  900°;  at  the  depth  of  30  miles  about  2700°,  and  so  on.  Iron 
melts  at  the  surface  of  the  Earth  (where  it  is  free  from  great  pressure) 
at  about  3000°.  If  the  substances  in  the  Earth's  interior  were  free 
from  pressure  the  interior  would  be  a  fluid  mass,  and  there  would  be 
great  tides  in  this  interior  ocean.  Astronomical  observations  show 
that  there  are  no  such  tides,  whence  it  follows  that  the  interior  of 
the  Earth  is,  on  the  whole,  solid.  There  are  many  reservoirs  of 
melted  rocks  (lavas)  no  doubt  in  the  neighborhood  of  volcanoes,  but 
on  the  whole  the  Earth  is  solid  and  about  as  stiff  as  a  globe  of  steel. 
The  spheroidal  shape  of  the  Earth  seems  to  show  that  it  once  was  in 
a  fluid  condition,  for  a  rotating  mass  of  fluid  will  take  the  form  of  a 
spheroid.  It  will  be  flattened  at  the  poles.  Its  meridians  will  be 
ellipses.  This  is  the  shape,  not  only  of  the  Earth,  but  of  all  the 
planets, 


242  ASTRONOMY. 

All  the  heat  of  the  Earth  comes  to  it  from  the  Sun.  The  Sun 
sends  its  heat  out  in  all  directions  along  every  possible  line  that  can 
be  drawn  from  the  San  outwards.  The  Sun  would  warm  the  whole 
interior  surface  of  a  sphere  93,000,000  miles  in  diameter  just  as 
much  as  it  now  warms  the  Earth  which  occupies  one  small  point 
of  such  a  sphere.  So  far  as  mankind  is  concerned  all  the  heat  that 
does  not  fall  on  the  Earth  is  lost.  The  Earth  receives  only  the 
minutest  fraction  of  it  (not  more  than  ju^tfcVinnnF)' 

Atmosphere  of  the  Earth. — The  Earth  is  surrounded  by  an  ocean  of 
water  in  which  the  attractions  of  the  Sun  and  Moon  produce  tides. 
It  is  likewise  surrounded  by  an  ocean  of  air,  and  in  this  atmosphere 
slight  tides  are  also  observed.  The  effect  of  the  atmosphere  on  the 
climates  of  the  Earth  is  most  important,  and  it  is  treated  in  works 
on  Meteorology. 

Astronomy  is  chiefly  concerned  with  the  effects  of  the  Earth's 
atmosphere  in  producing  a  refraction  (a  bending)  of  the  rays  of  light 
that  reach  us  from  the  stars  so  that  we  do  not  see  them  quite  in 
their  true  directions.  The  atmosphere  of  the  Earth  surrounds  it  to  a 
height  of  a  hundred  miles  or  more.  Its  heavier  layers  are  nearest 
the  Earth's  surface.  Even  at  a  height  of  3  or  4  miles  there  is 
scarcely  enough  air  for  breathing. 

Refraction  of  Light  by  the  Atmosphere. — In  figure  153 
0  is  the  centre  of  the  Earth  and  A  the  station  of  an 
observer  on  its  surface.  8  is  a  star.  If  there  were  no 
atmosphere  the  observer  would  see  the  star  along  the  line 
AS.  But  the  atmosphere  acts  like  a  lens  and  bends 
(refracts)  the  light  from  the  star  along  the  curved  line 
6,  dy  c,  #,  a,  and  the  light  from  the  star  comes  to  the 
observer  along  the  line  AS'.  He  sees  the  star  projected  on 
the  celestial  sphere  at  $',  therefore,  and  not  in  its  true 
place  S.  The  star  is  (apparently)  thrown  nearer  to  his 
zenith  by  refraction.  It  will  rise  sooner  and  set  later, 
therefore,  on  this  account. 

At  the  zenith  the  refraction  is  0,  at  45°  zenith  distance  tLe  refrac- 
tion is  1',  and  at  90°  it  is  34'  30".  The  ravs  of  light  traverse  greater 
thicknesses  of  air  at  large  zenith  distances  and  are  more  refracted 
therefore.  Stars  at  the  zenith  distances  of  45°  and  90°  appear  ele- 
vated above  their  true  places  by  1'  and  34£'  respectively.  If  the  sun 
has  just  risen — that  is,  if  its  lower  edge  is  just  in  apparent  contact 


THE  EARTH.  243 

with  the  horizon — it  is  in  fact  entirely  below  the  true  horizon,  for 
the  refraction  (35')  has  elevated  its  centre  by  moie  than  its  whole 
apparent  diameter  (32'). 

The  moon  is  full  when  it  is  exactly  opposite  the  sun,  and  therefore, 
were  there  no  atmosphere,  moon-rise  of  a  full  moon  and  sunset 
would  be  simultaneous.  In  fact,  both  bodies  being  elevated  by 
refraction,  we  see  the  full  moon  risen  before  the  sun  has  set. 


FIG.  153. — REFRACTION  OF   THE  LIGHT  OF  A   STAR  BY  THE 
EARTH'S  ATMOSPHERE. 

Twilight. — It  is  plain  that  one  effect  of  refraction  is  to 
lengthen  the  duration  of  daylight  by  causing  the  Sun  to 
appear  above  the  horizon  before  the  time  of  his  geometrical 
rising  and  after  the  time  of  true  sunset. 

Daylight  is  also  prolonged  by  the  reflection  of  the  Sun's 
rays  (after  sunset  and  before  sunrise)  from  the  small 
particles  of  matter  suspended  in  the  atmosphere.  This 
produces  a  general  though  faint  illumination  of  the  atmos 
phere,  just  as  the  light  scattered  from  the  floating  particles 
of  dust  illuminated  by  a  sunbeam  let  in  through  a  crack  in 
a  shutter  may  brighten  the  whole  of  a  darkened  room. 


244:  ASTRONOMY. 

The  Sun's  direct  rays  do  not  reach  an  observer  on  the 
Earth  after  the  instant  of  sunset,  since  the  solid  body  of 
the  Earth  intercepts  them.  But  the  Sun's  direct  rays 
illuminate  the  clouds  of  the  upper  air,  and  are  reflected 
downwards  so  as  to  produce  a  general  illumination  of  the 
atmosphere,  which  is  called  twilight. 

In  the  figure  let  A  BCD  be  the  Earth  and  A  an  observer 
on  its  surface,  to  whom  the  Sun  8  is  just  setting.  Aa  is 


FIG.  154. — THE  PHENOMENA  OF  TWILIGHT. 

the  horizon  of  A-,  Bb  of  B\  Cc  of  (7;  Dd  of  D.  Let  the 
circle  PQR  represent  the  upper  layer  of  the  atmosphere. 
Between  ABCD  and  PQR  the  air  is  filled  with  suspended 
particles  that  reflect  light.  The  lowest  ray  of  the  Sun, 
SAM,  just  grazes  the  Earth  at  A]  the  higher  rays  8N and 
SO  strike  the  atmosphere  above  A  and  leave  it  at  the  points 
Q  and  R. 

Each  of  the  lines  SAPM,  SQN\$  bent  from  a  straight 
course  by  refraction,  but  SRO  is  not  bent  since  it  just 


THE  EARTH.  245 

touches  the  upper  limits  of  the  atmosphere.  The  space 
MABCDE  is  the  Earth's  shadow.  An  observer  at  A 
receives  the  (last)  direct  rays  from  the  Sun,  and  also  has 
his  sky  illuminated  by  the  reflection  from  all  the  particles 
lying  in  the  space  PQRT  which  is  all  above  his  horizon  Aa. 

An  observer  at  B  receives  no  direct  rays  from  the  Sun. 
It  is  after  his  sunset.  Nor  does  he  receive  any  light  from 
that  portion  of  the  atmosphere  below  APM\  but  the  por- 
tion PRx,  which  lies  above  his  horizon  Bl)  is  lighted  by  the 
Sun's  rays,  and  reflects  some  light  to  B.  The  twilight  is 
strongest  at  R,  and  fades  away  gradually  towards  P.  The 
altitude  of  the  twilight  at  B  is  bd. 

To  an  observer  at  C  the  twilight  is  derived  from  the 
illumination  of  the  portion  PQz  which  lies  above  his 
horizon  Cc.  The  altitude  of  the  twilight  at  C  is  cd. 

To  an  observer  at  D  it  is  night.  All  of  the  illuminated 
atmosphere  is  below  his  horizon  Dd. 

The  twilight  arch  is  more  marked  in  summer  than  in  winter ;  in 
high  latitudes  than  in  low  ones.  There  is  no  true  night  in  Scotland 
at  midsummer,  for  example,  the  morning  twilight  beginning  before 
the  evening  twilight  has  ended  ;  and  in  the  torrid  zone  there  is  no 
perceptible  twilight.  Twilight  ends  when  the  Sun  reaches  a  point 
about  20°  below  the  horizon.  The  student  should  observe  the 
phenomena  of  twilight  for  himself.  It  is  best  seen  in  the  country, 
shortly  after  sunset,  as  far  away  from  city  lights  as  may  be. 

Astronomical  Measures  of  Time  to  the  Inhabitants  of  the 
Earth. — The  simplest  unit  of  time  is  the  sidereal  day,  that 
is  the  interval  of  time  required  for  the  Earth  to  turn  once 
on  its  axis.  It  is  measured  by  the  interval  between  two 
successive  transits  of  the  same  star  over  the  observer's 
meridian ;  and  it  is  divided  into  24  sidereal  hours. 

The  most  obvious  unit  of  time  is  the  (apparent)  solar 
day,  that  is  the  interval  of  time  between  two  successive 
transits  of  the  true  Sun  over  the  observer's  meridian.  AB 
apparent  solar  days  are  not  equal  in  length,  a  more  con- 


246  ASTRONOMY. 

venient  unit  has  been  devised,  that  is  the  mean  solar  day, 
which  is  the  interval  of  time  between  LAVO  successive 
transits  of  the  mean  San  (see  page  90)  over  the  observer's 
meridian.  The  relation  between  the  sidereal  and  mean 
solar  day  has  been  previously  given  (page  95)  and  is  as 
below : 

366.24222  sidereal  days  =  365.24222  mean  solar  days, 

I  sidereal  day  =      0.997  mean  solar  day, 
24  sidereal  hours  =         23h  56m  4".  091  mean  solar  time, 
1  mean  solar  day  =      1.03  sidereal  days, 
24  mean  solar  hours  =         24h  3m  56'.555  sidereal  time. 

The  quantity  to  be  added  to  (or  subtracted  from)  ap- 
parent solar  time  to  obtain  mean  solar  time  is  calculated 
beforehand  and  printed  in  the  Nautical  Almanac  under 
the  heading  "  Equation  of  Time."  (See  page  151.) 

The  months  now  or  heretofore  jn  use  among  the  peoples 
of  the  globe  may  for  the  most  part  be  divided  into  two 
classes : 

(1)  The  lunar  month   pure  and   simple,  or  the   mean 
interval  between  successive  new  Moons. 

(2)  An  approximation  to  the  twelfth   part  of  a  year, 
without  respect  to  the  motion  of  the  Moon. 

The  mean  internal  between  consecutive  new  Moons  being 
nearly  29£  days,  it  was  common  in  the  use  of  the  pure  lunar 
month  to  have  months  of  29  and  30  days  alternately. 

The  interval  between  two  successive  returns  of  the  Sun 
to  the  same  star  is  called  the  sidereal  year.  Its  length  is 
found  by  observation  to  be 

365  (mean  solar)  days  6  hours  9  minutes  9  seconds  =  365d. 25636. 

The  interval  between  two  successive  returns  of  the  Sun  to 
the  same  equinox  is  called  the  equinoctial  year.  Its  length 
is  found  by  observation  to  be 

365  (mean  solar)  days  5  hours  48  minutes  46  seconds  =  365d.  24220. 


THE  EARTH.  247 

The  sidereal  year  measures  the  time  of  the  revolution  of 
the  Earth  in  her  orbit.  The  equinoctial  year  governs  the 
recurrence  of  the  seasons,  because  the  seasons  depend  on 
the  Sun's  declination  (see  page  175)  and  the  declination 
changes  from  south  to  north  at  the  vernal  equinox — at  the 
passage  of  the  Sun  across  the  celestial  equator. 

The  solar  year  of  365£  days  has  been  a  unit  of  time- 
reckoning  from  very  early  times.  Four  such  years  are 
equal  to  1461  days.  The  cycle  of  four  years,  three  of  them 
of  365  days  and  the  fourth  of  366,  which  we  use,  was 
adopted  in  China  in  the  remotest  historic  times. 

The  Julian  Calendar. — The  chil  calendar  now  in  use 
throughout  Christendom  had  its  origin  among  the  Romans, 
and  its  foundation  was  laid  by  JULIUS  C^SAB.  Before  his 
time,  Rome  can  hardly  be  said  to  have  had  a  chronological 
system.  The  length  of  the  year  was  not  prescribed  by  any 
invariable  rule,  and  it  was  changed  from  time  to  time  to 
suit  the  caprice  or  to  compass  the  ends  of  the  rulers. 

Instances  of  this  tampering  disposition  are  familiar  to  the  histori- 
cal student.  It  is  said,  for  instance,  that  the  Gauls  having  to  pay  a 
certain  monthly  tribute  to  the  Romans,  one  of  the  governors  ordered 
the  year  to  be  divided  into  14  months,  in  order  that  the  pay-days 
might  recur  more  rapidly.  CAESAR  fixed  the  year  at  365  days,  with 
the  addition  of  one  day  to  every  fourth  year.  The  old  Roman  months 
were  afterwards  adjusted  to  the  Julian  year  in  such  a  way  as  to  give 
rise  to  the  somewhat  irregular  arrangement  of  months  which  we  now 
have.  The  names  of  our  days  are  partly  from  Roman,  partly  from 
Scandinavian  mythology.  The  student  should  consult  a  dictionary 
for  the  derivations  of  their  names. 

Old  and  New  Styles.— The  mean  length  of  the  Julian  year  is  about 
11£  minutes  greater  than  that  of  the  equinoctial  year,  which  measures 
the  recurrence  of  the  seasons.  This  difference  is  of  little  practical 
importance,  as  it  only  amounts  to  a  week  in  a  thousand  years,  and  a 
change  of  this  amount  in  that  period  can  cause  no  inconvenience. 
But,  in  order  to  have  the  year  as  correct  as  possible,  two  changes 
were  introduced  into  the  calendar  by  Pope  GREGORY  XIII.  with  this 
object.  It  was  decreed  that 


248  ASTRONOMY. 

(1)  The  day  following  October  4,  1582,  was  to  be  called  the  15th 
instead  of  the  5th,  thus  advancing  the  count  10  days. 

(2)  The  closing  year  of  each  century,  1600,   1700,  etc.,  instead  of 
being  always  a  leap-year,  as  in  the  Julian  calendar,  was  to  be  such 
only  when  the  number  of  the  century  is  divisible  by  4.     Thus  while 
1600  remained  a  leap-year,  as  before,  1700,  1800,  and  1900  were  to  be 
common  years. 

This  change  in  the  calendar  was  speedily  adopted  by  all  Catholic 
countries,  and  more  slowly  by  Protestant  ones,  England  holding  out 
until  1752.  In  Russia,  the  Julian  calendar  is  still  continued  without 
change.  The  Russian  reckoning  is  therefore  12  days  behind  ours, 
the  ten  days  dropped  in  1582  being  increased  by  the  days  dropped 
from  the  years  1700  and  1800  in  the  new  reckoning.*  The  modified 
calendar  is  called  the  Gregorian  Calendar,  or  New  Style,  while  the 
old  system  is  called  the  Julian  Calendar,  or  Old  Style. 

It  is  to  be  remarked  that  the  practice  of  commencing  the  year  on 
January  1st  was  not  universal  until  comparatively  recent  times.  The 
most  common  times  of  commencing  were,  perhaps,  March  1st  and 
March  22d,  the  latter  being  the  time  of  the  vernal  equinox.  But 
January  1st  gradually  made  its  way,  and  became  universal  after  its 
adoption  by  England  in  1752. 

Precession  of  the  Equinoxes. — It  has  just  been  said  that 
observation  proves  the  sidereal  year  to  have  a  length  of 
365.25636  mean  solar  days,  and  the  equinoctial  year  to 
have  a  length  of  365.24220  days.  The  Sun  in  his  annual 
circuit  of  the  heavens  moves  from  a  star  to  the  same  star 
again  in  the  sidereal  year,  from  an  equinox  to  the  same 
equinox  again  in  the  equinoctial  year. 

As  the  stars  are  fixed,  the  Sun's  revolution  around  the 
ecliptic  from  star  back  to  the  same  star  again  must  be  a 
revolution  through  exactly  360°  0'  0"  of  right-ascension. 
As  the  equinoctial  year  is  shorter  than  the  sidereal  year, 
the  Sun's  revolution  from  equinox  t©  equinox  must  be  a 
revolution  through  an  angle  slightly  less  than  360°. 

(    8W.8MM    )  ;   (       MP.MBN)      . 

(  sidereal  year  )       (  equinoctial  year ) 

The  equinox  must  therefore  be  moving  in  space  so  that 
*  Russia  will  adopt  the  New  Style  in  A.D.  1901 


THE  EARTH.  249 

v  when  it  is  met  a  second  time  the  Sun  has  made  one  revoln- 

v  tion   less   50".      The  Sun's  annual  circuit   is   performed 

among  the  stars  from  west  to  east.     The  equinox  therefore 

moves  (to  meet  the  Sun)  westward  in  right-ascension  at  the 

rate  of  about  50"  per  year. 


FIG.   155. — THE  CELESTIAL  EQUATOR   (AD)  AND    THE   ECLIPTIC 
(CD) ;  E,  is  THE  VERNAL  EQUINOX. 

The  equinox  (E  in  the  figure)  is  nothing  but  the  point 
where  the  ecliptic  (CD)  intersects  the  celestial  equator 
(AB).  If  their  point  of  intersection  changes  it  must  be 
because  one  or  both  of  these  circles  is  moving.  If  the  plane 
of  the  celestial  equator  is  moving  the  declinations  of  all  the 
stars  will  change  from  year  to  year.  Observation  shows 
that  the  declinations  do  change  slightly  from  year  to  year.* 
If  the  plane  of  the  ecliptic  is  fixed  the  celestial  latitudes  of 
all  the  stars  (their  angular  distances  from  the  ecliptic)  will 
not  change  from  year  to  year.  Observation  shows  that 

*The  right-ascensions  also  change  slightly  because  the  equinox, 
which  is  the  origin  of  R  A.,  is  moving.  The  effect  of  annual  pre- 
cession on  the  places  of  stars  is  given  in  the  fourth  and  sixth  columns 
of  Table  V  at  the  end  of  this  book. 


250  ASTRONOMY. 

while  the  declinations  of  all  the  stars  do  change  annually 
by  small  amounts  their  celestial  latitudes  do  not  change. 
Hence  the  plane  of  the  ecliptic  is  fixed;  and  hence  the 
westward  motion  of  the  equinox  is  entirely  due  to  a  motion 
of  the  plane  of  the  celestial  equator. 

If  the  plane  of  a  circle  of  the  celestial  sphere  is  fixed  the 
place  of  the  pole  of  that  circle  on  the  celestial  sphere  is 
stationary.  The  ecliptic  (CD)  is  fixed  (see  the  figure),  and 
hence  the  place  of  its  pole  (Q)  among  the  stars  is  station- 
ary. If  the  pole  of  the  ecliptic  is  10°  from  a  star  in  1800 
it  will  be  10°  from  that  star  in  1900.  On  the  other  hand, 
if  the  plane  of  the  celestial  equator  (AB)  is  moving,  as  it 
is,  the  place  of  its  pole  (P)  among  the  stars  must  be 
moving.  The  north  pole  of  the  heavens  is  now  near  to 
Polaris,  but  it  will  in  time  move  away  from  it.  At  the 
time  when  the  pyramids  were  built,  about  B.C.  2700, 
Polaris  was  not  the  "  north-star,"  but  the  star  Alpha 
Draconis  (see  star-map  No.  VI). 

The  pole  of  the  ecliptic  (Q)  is  fixed;  the  pole  of  the 
celestial  equator  (P)  is  moving.  The  angle  between  the 
plane  of  the  ecliptic  and  the  plane  of  the  celestial  equator 
(POQ  =  23%°)  does  not  change.  Therefore  the  pole  P 
must  revolve  about  the  fixed  pole  Q  in  a  circle.  The  in- 
clination of  the  two  planes  CD  and  AB  will  not  be  changed 
by  such  a  revolution,  but  their  line  of  intersection  (EF) 
will  move  slowly  round  the  celestial  sphere.  Their  line  of 
intersection  is  the  line  joining  the  two  equinoxes.  The 
annual  motion  of  the  equinox  is,  as  we  have  seen,  50"  of 
arc,  so  that  in  about  25,920  years  the  equinox  (E)  will 
move  completely  around  the  circle  of  the  ecliptic  and  will 
return  to  its  starting-point.  In  the  same  period  the  pole 
of  the  celestial  equator  (P)  will  move  in  a  circle  completely 
around  the  pole  of  the  ecliptic  (Q). 

25,920  X  50"  —  1,296,000"  =  360°. 


THE  EARTH. 


251 


The  student  can  trace  the  path  of  the  north  pole  of  the  heavens 
among  the  stars  on  Star-map  No.  IV,  following.  Turning  this  map 
upside-down  let  him  find  the  constellations  Draco,  Ursa  minor, 
Cepheus,  Cygnus,  and  Lyra. 

About  3000  years  ago  the  pole  was  near  a  in  Draco, 
At  the  present  time  the  pole  is  near  a  in  Ursa  minor, 
About  2000  years  hence  the  pole  will  be  very  near  to  a: in  Ursa  minor, 
"     4000      "         "       "       "       "     "  near  y  in  Ceplieus, 
"     7500      "        "       "       "      "     "     "    a  in 
"    11500     "        "       "       "      "     "     "    d   in  Cygnus, 
"    14000      "         "       "       "      "     "     "    am  Lyra. 

If  he  has  a  celestial  globe  at  hand  he  will  find  the  path  of  the 
north  pole  of  the  heavens  about  the  north  pole  of  the  ecliptic  marked 
down  among  the  stars. 


FIG.  156.— THE  SEASONS  ON  THE  EARTH. 


The  effects  of  the  motion  of  the  pole  of  the  heavens  on  our  sea- 
sons may  be  studied  in  the  figure.  The  figure  represents  the  Earth  in 
four  positions  during  its  annual  revolution.  Its  axis  inclines  to  the 
right  in  each  of  these  positions.  In  Chapter  VIII  it  was  said  that 
the  Earth's  axis  always  remained  parallel  to  itself.  The  phenomena 
of  precession  show  that  this  is  not  absolutely  true,  but  that,  in  real- 
ity, the  direction  of  the  axis  is  changing  with  extreme  slowness. 
After  the  lapse  of  some  6400  years,  the  north  pole  of  the  Earth,  as 
represented  in  the  figure,  will  not  incline  to  the  right,  but  towards 


252  ASTRONOMY. 

the  reader,  the  amount  of  the  inclination  remaining  nearly  the 
same.  The  result  will  evidently  be  a  shifting  of  the  seasons.  At  D 
we  shall  have  the  winter  solstice,  because  the  north  pole  will  be  in- 
clined towards  the  reader  and  therefore  from  the  Sun,  while  at  A 
we  shall  have  the  vernal  equinox  instead  of  the  winter  solstice,  and 
so  on. 

In  6400  years  more  the  north  pole  will  be  inclined  towards  the  left, 
and  the  seasons  will  be  reversed.  Another  interval  of  the  same 
length,  and  the  north  pole  will  be  inclined  from  the  reader,  the 
seasons  being  shifted  through  another  quadrant.  Finally,  at  the 
end  of  about  25,900  years,  the  axis  will  have  resumed  its  original 
direction. 


FIG.  157.— THE  EARTH'S  Axis  AND  EQUATOR. 

The  north  pole  of  the  heavens  is  the  point  where  the 
celestial  sphere  is  met  by  the  axis  of  the  Earth  prolonged. 
The  celestial  equator  is  the  plane  of  the  terrestrial  equator 
produced.  The  axis  of  the  Earth  does  not  move  relatively 
to  the  Earth's  crust.  The  Earth's  equator  always  passes 
through  the  same  countries  —  Ecuador,  Brazil,  Africa, 


THE  EARTH.  253 

Sumatra.  The  latitudes  of  places  on  the  Earth  do  not 
change.  Precession  is  not  due  to  a  motion  of  the  Earth's 
axis  simply,  but  to  a  motion  of  the  whole  Earth  that  carries 
the  axis  with  it. 


FIG.  158.— DIAGRAM  TO  ILLUSTRATE  THE  CAUSE  OP  PRECESSION. 


THE  CAUSE  OF  PRECESSION. 

The  cause  of  precession,  etc.,  is  illustrated  in  the  figure,  which 
shows  a  spherical  Earth  surrounded  by  a  ring  of  matter  at  the  equa- 
tor. If  the  Earth  were  really  spherical  there  would  be  no  precession. 
It  is,  however,  ellipsoidal  with  a  protuberance  at  the  equator.  The 
effect  of  this  protuberance  is  to  be  examined.  Consider  the  action 
between  the  Sun  and  Earth  alone.  If  the  ring  of  matter  were  absent, 
the  Earth  would  revolve  about  the  Sun  as  is  shown  in  Fig.  156 
(Seasons). 

The  Sun's  North  Polar  Distance  is  90°  at  the  equinoxes,  and  66|* 
and  113^°  at  the  solstices.  At  the  equinoxes  the  Sun  is  in  the  direc- 
tion Cm ;  that  is,  NCm  is  90°.  At  the  winter  solstice  the  Sun  is  in 
the  direction  Cc  ;  NCc  =  113£°.  It  is  clear  that  in  the  latter  case  the 
effect  of  the  Sun  on  the  ring  of  matter  will  be  to  pull  the  Earth 
downwards  so  that  the  direction  Cm  tends  to  become  the  direction  Cc. 
An  opposite  effect  will  be  produced  by  the  Sun  when  its  polar  dis- 
tance is  66£°. 

The  Moon  also  revolves  round  the  Earth  in  an  orbit  inclined  to  the 
equator,  and  in  every  position  of  the  Moon  it  has  a  different  action 
on  the  ring  of  matter.  The  Earth  is  all  the  time  rotating  on  its  axis, 
and  these  varying  attractions  of  Sun  and  Moon  are  equalized  and 
distributed  since  different  parts  of  the  Earth  are  successively  pre- 
sented to  the  attracting  body.  The  result  of  all  the  complex  motions 


254  ASTRONOMY. 

we  have  described  is  a  conical  motion  of  the  Earth's  axis  NC  about 
the  line  CE. 

The  Earth's  shape  is  of  course  not  that  given  in  the  figure,  but  an 
ellipsoid  of  revolution.  The  ring  of  matter  is  not  confined  to  the 
equator,  but  extends  away  from  it  in  both  directions.  The  effects  of 
the  forces  acting  on  the  Earth  as  it  is  are,  however,  similar  to  the 
effects  just  described.  The  motion  of  precession  is  not  uniform,  but 
is  subject  to  several  small  inequalities  which  are  called  nutation. 

The  fact  of  precession  was  discovered  by  HIPPARCHUS 
more  than  2000  years  ago.  He  observed :  (1)  That  the  Sun 
made  a  revolution  from  equinox  to  equinox  in  a  shorter 
time  than  that  required  for  its  revolution  from  star  to  star. 

(2)  As  the  stars  were  fixed  the  equinox  must  be  moving. 

(3)  The  equinox  is  the  intersection  of  the  ecliptic  and  the 
celestial  equator,  and  hence  one  or  both  of  these  planes 
must  be  moving.     (4)  The  ecliptic  was  not  moving  because 
the  celestial  latitudes  of  stars  did  not  change.     (5)  The 
celestial  equator  was  in  motion  because  the  declinations  of 
all  the  stars  (and  their  right-ascensions  also)  did  change. 
This  was  a  mighty  discovery,  and  it  required  a  genius  of 
the  first  order  to  make  it. 

COPERNICUS,  in  1543,  declared  that  precession  was  due 
to  a  conical  motion  of  the  Earth's  axis  of  rotation  about 
the  line  joining  the  Earth's  centre  with  the  pole  of  the 
ecliptic. 

NEWTON,  in  1687,  worked  out  the  complete  explanation. 
This  could  not  possibly  have  been  done  until  the  theory  of 
gravitation  was  thoroughly  understood  nor  until  the  science 
of  mathematics  had  been  developed  (by  NEWTON'S  own 
researches)  to  a  high  point.  Three  of  the  greatest  names 
of  science  are  associated  in  this  discovery. 

The  Progressive  Motion  of  Light, — GALILEO  made  ex- 
periments to  determine  whether  light  required  time  to  pass 
from  one  place  to  "another.  His  methods  were  not  suffi- 
ciently refined  to  decide  the  question,  but  the  subject  was 
not  lost  sight  of.  In  the  year  1675,  OLAUS  ROMER,  a 


THE  EARTH.  255 

Danish  astronomer  (to  whom  we  owe  the  invention  of  the 
transit  instrument,  among  other  things),  was  engaged  in 
making  tables  of  the  times  of  the  eclipses  of  the  satellites 
of  Jupiter. 


FIG.   159. — THE   ECLIPSES    OF   JUPITER'S    SATELLITES   AND  THE 
PROGRESSIVE  MOTION  OF  LIGHT. 

S,  is  the  Sun  :  T,  is  the  Earth  in  its  orbit;  J,  is  Jupiter  in  opposition  with 
the  Sun ;  J'"  is  Jupiter  in  conjunction  with  the  Sun. 

The  figure  shows  the  Earth  at  T.  When  Jupiter  is  at  J 
it  is  nearest  to  the  Earth ;  when  Jupiter  is  at  J '"  (and  the 
Earth  at  T}  the  two  bodies  are  as  far  apart  as  possible. 
TJ"r  is  larger  than  TJ  by  the  diameter  of  the  Earth's 
orbit;  by  about  186,000,000  miles  therefore.  Jupiter 
casts  a  long  shadow  (see  the  cut)  and  one  of  its  satellites 
(its  orbit  is  the  small  circle  about  /  and  about  J"f)  is 
eclipsed  at  every  revolution.  ROMER  calculated  the  times 
at  which  an  observer  on  the  Earth  would  see  such  eclipses. 
He  found  that  his  tables  could  be  reconciled  with  observa- 
tion only  by  supposing  that  the  light  from  the  satellite 
required  time  to  pass  from  Jupiter  to  the  Earth,  When 
Jupiter  is  at /its  light  has  to  pass  over  the  luieJT  to 
reach  the  Earth.  When  Jupiter  is  at  J'"  its  light  has  to 
pass  over  the  longer  line  J '"  T.  Accurate  observations  show 
that  eclipses  of  the  satellites  are  seen  16  minutes  38  seconds 
earlier  when  the  planet  is  at  ./  than  when  it  is  at  «/'". 
Light  requires  16m  388  to  pass  over  the  diameter  of  the 
Earth's  orbit,  therefore,  or  8m  19"  to  pass  over  the  radius  of 
the  orbit. 


256  ASTRONOMY. 

In  4998  light  travels  92,900,000  miles,  or  at  the  rate  of 
186,200  miles  in  one  second  of  time.*  The  sunlight  is 
499  seconds  old  when  it  reaches  the  Earth.  As  the  velocity 
of  light  is  uniform  it  follows  that  (approximately): 

Sunlight  is        3m  old  when  it  reaches  Mercury, 


" 

"         6m   "       "     " 

**       Venus, 

ft 

(t            gm     <t           ((       a 

"      Earth, 

(I 

«         13m     <c           «        « 

"      Jf«r5, 

if 

it       ,4_'5"'    ''        *'      '' 

4<      Jupiter, 

«  lh  19m     it          it       tt 

4  k      Saturn, 

" 

<<2h38m   "       "     " 

"      Uranus, 

" 

"4h    8m  "       ff     " 

"      Neptune. 

The  time  required  for  the  light  of  a  planet  to  reach  the  Earth  is 
called  the  planet's  aberration-time.  For  instance,  the  aberration-t.me 
of  Neptune  is  about  4h  8m.  This  means  that  the  light  by  which 
we  see  Neptune  now — this  instant — is  4h  8m  old  when  it  reaches  us. 
Neptune  may  hare  vanished  4U  7m  ago  for  all  we  know.  We  can  only 
find  out  by  waiting.  The  stars  are  very  much  further  away  than 
Neptune.  We  shall  see,  later  on,  that  the  light  of  even  the  nearest 
star  is  more  than  4  years  on  its  passage  to  the  Earth.  The  light  from 
Polaris  takes  more  than  40  years  to  reach  us.  Polaris  may  have 
vanished  40  years  ago  for  all  we  know— now  ;  we  can  only  find  out 
by  waiting.  Only  a  very  few  of  the  stars  are  so  near  as  this.  Most 
of  them  are  immensely  further  away. 

The  theory  of  ROMER  was  not  fully  accepted  by  his  contemporaries. 
The  velocity  of  light  was  so  much  greater  than  any  known  terres- 
trial velocity  that  it  seemed  difficult  to  accept  it.  Even  the  motion 
of  the  Earth  in  its  orbit  was  only  18 J  miles  per  second,  The  velocity 
of  light  was  10,000  times  as  large.  In  the  year  1729  JAMES  BRADLEY, 
afterwards  Astronomer  Royal  of  England,  observed  a  phenomenon  of 
a  different  character  that  entirely  confirmed  ROMER'S  conclusions. 
BRADLEY  discovered  that  the  stars  are  not  seen  in  their  true  places, 
but  that  each  star  is  displaced  by  a  small  angle  (never  more  than 
21").  This  displacement  occurs  because  the  Earth  is  moving  among 
the  stars  with  a  velocity  that  is  comparable  with  the  velocity  of  light. 

In  the  figure  suppose  AB  to  be  the  axis  of  a  telescope,  8  a 
star,  and  SAB'  a  ray  of  light  which  emanates  from  the  star.  The 

*  The  most  accurate  determinations  give  186,330  miles. 


ABERRATION.  257 

student  may  imagine  AB  to  be  a  rod  which  au  observer  at  B  seeks 
to  point  at  the  star  8.  It  is  evident  that  he  must  point  this  rod  in 
such  a  way  that  the  ray  of  light  shall  run 
accurately  along  its  length.  If  the  observer 
(and  the  Earth)  were  at  rest  at  B  he  will 
point  the  rod  along  the  line  SB. 

Suppose  now  that  the  observer  (and  the 
Earth)  are  moving  from  B  toward  B'  witli 
such  a  velocity  that  he  moves  from  B  to 
B'  during  the  time  required  for  a  ray  of 
light  to  move  from  A  to  B'.  Suppose, 
also,  that  the  ray  of  light  from  8  (SA) 
reaches  A  at  the  same  time  that  the  end  of 
his  rod  does.  Then  it  is  clear  that  while 
the  rod  is  moving  from  the  position  AB 
to  the  position  A'B',  the  ray  of  light  will  FIG.  156. 

move  from  A  to  B,  and  will  therefore  run    accurately  along   the 
length  of  the  rod. 

For  instance,  if  b  is  one  third  of  the  way  from  B  to  B',  then  the 
light,  at  the  instant  when  the  rod  takes  the  position  &«,  will  be  one 
third  of  the  way  from  A  to  R ,  and  will  therefore  be  accurately  on 
the  rod.  Consequently,  to  the  observer,  the  rod  will  appear  to  be 
pointed  at  the  star.  In  reality,  however,  the  pointing  will  not  be  in 
the  true  direction  of  the  star,  but  will  deviate  from  it  by  a  certain 
angle  depending  upon  the  ratio  of  the  velocity  with  which  the 
observer  is  carried  along  to  the  velocity  of  light. 

If  the  Earth,  stood  still  there  would  be  no  aberration.  If  the 
velocity  of  light  were  10,000  times  greater  than  it  is  the  aberration 
would  be  vanishingly  small. 

Effects  of  Aberration.— The  velocities  of  light  and  of  the  Eartli 
being  what  they  are,  the  apparent  displacement  of  a  star's  position, 
due  to  aberration  is  always  less  than  21". 

Aberration  phenomena  can  be  observed  on  the  Earth 
on  any  rainy  day  with  no  wind.  (See  fig.  157.)  The 
rain-drops  descend  vertically.  If  the  observer  stands  still 
he  must  hold  his  umbrella  straight  above  his  head.  Now 
let  him  walk  briskly  towards  the  south.  He  will  find  that 
he  must  incline  his  umbrella  southwards  (in  the  direction 
of  his  motion)  to  protect  himself.  If  he  walks  towards  the 
west  he  must  incline  his  umbrella  westwards  (in  the 


258  ASTRONOMY. 

direction  of  his  motion).  If  instead  of  walking  he  runs, 
the  same  effects  are  produced,  only  he  will  find  that  he 
must  incline  his  umbrella  still  more.  All  this  while  each 
rain-drop  is  falling  vertically  ;  yet  every  change  of  his 
direction  of  motion  and  of  his  velocity  (relative  to  the 
velocity  of  the  falling  drops  of  rain)  requires  him  to  alter 
the  inclination  of  his  protecting  umbrella.  The  experiment 
is  so  easy  that  the  student  should  not  fail  to  try  it. 

—  What  is  the  Earth's  distance  from  the  Sun?  (Answer,  about 
93,000,000  miles.)  Do  the  seasons  depend  on  the  Earth's  proximity 
to  the  Sun?  What  is  the  shape  of  the  Earth?  How  is  the  figure  of 
the  Earth  determined?  Define  the  mass,  the  density,  the  volume 
of  a  body.  Define  the  weight  of  a  body.  Does  a  body — say  a  cubic 
inch  of  copper — weigh  the  same  in  Brazil  and  in  Iceland  ?  If  you 
could  take  it  10,000  miles  above  the  Earth  would  it  weigh  less  or 
more  than  in  New  York  ?  How  is  the  density  of  specimens  of  rocks 
determined  ?  How  is  the  density  of  the  whole  Earth,  considered  as 
one  mass,  determined  ?  Is  the  temperature  of  the  Earth  greater  10 
miles  below  the  surface  than  5  miles  deep  ?  Does  the  Earth  receive 
all  the  Sun's  heat?  What  is  the  refraction  of  light  by  the  Earth's 
atmosphere  ?  Does  refraction  increase  or  diminish  the  apparent  zenith 
distance  of  the  Sun?  Describe  the  phenomena  of  twilight?  Did 
you  ever  see  it  yourself?  Define  the  different  kinds  of  day.  What 
is  a  month?  Define  the  sidereal  and  the  equinoctial  year.  Which 
is  the  longer?  What  does  that  prove?  Will  Polaris  always  be  our 
pole-star?  What  is  the  cause  of  precession?  What  three  great 
names  are  connected  with  the  discoveries  regarding  precession  ?  and 
at  what  dates  ?  How  was  it  first  proved  that  light  required  time  to 
pass  from  place  to  place  ?  About  how  long  does  it  take  sunlight  to 
reach  the  Earth  ?  to  reach  Neptune?  About  how  long  does  it  require 
for  the  light  of  the  nearest  star  to  reach  the  Earth  ?  (Answer,  4 
years.) 


ABERRATION. 


259 


FIG   157.— EFFECTS  OF  ABERRATION. 


CHAPTER   XIV. 
CELESTIAL  MEASUREMENTS  OP  MASS  AND  DISTANCE. 

29.  The  Celestial  Scale  of  Measurement. — The  units  of 
length  and  mass  employed  in  Astronomy  are  necessarily 
different  from  those  used  in  daily  life.  The  distances  and 
magnitudes  of  the  heavenly  bodies  are  never  reckoned  in 
miles  or  other  terrestrial  measures  for  astronomical  pur- 
poses; when  so  expressed  it  is  only  for  the  purpose  of 
making  the  subject  clearer  to  the  general  reader.  The 
mass  of  a  body  may  be  expressed  in  terms  of  that  of  the 
Sun  or  of  the  Earth,  but  never  in  kilogrammes  or  tons, 
unless  in  popular  language. 

There  are  two  reasons  for  this  course.  One  is  that  in 
most  cases  celestial  distances  have  first  to  be  determined  in 
terms  of  some  celestial  unit — the  Earth's  distance  from  the 
Sun,  for  instance — and  it  is  more  convenient  to  retain  this 
unit  than  to  adopt  a  new  one.  The  other  is  that  the 
values  of  celestial  distances  in  terms  of  ordinary  terrestrial 
units  are  more  or  less  uncertain,  while  the  corresponding 
values  in  astronomical  units  are  known  with  great  accuracy. 

An  example  of  this  practice  is  afforded  when  we  deter- 
mine the  dimensions  of  the  solar  system.  By  a  series  of 
observations  of  their  positions  on  different  dates,  investi- 
gated by  means  of  KEPLER'S  laws  and  the  theory  of 
gravitation,  it  is  possible  to  determine  the  forms  of  the 
planetary  orbits,  the  positions  of  their  planes,  and  their 
relative  dimensions,  with  great  precision. 

KEPLER'S  third  law  enables  us  to  determine  the  mean 
distance  of  a  planet  from  the  Sun  when  we  know  its 

260 


CELESTIAL  MEASUREMENTS.  261 

period  of  revolution  (see  page  200).  All  the  major  planets, 
as  far  out  as  Saturn,  have  been  observed  throngh  so  many 
revolutions  that  their  periodic  times  can  be  determined  with 
great  exactness — in  fact  within  a  fraction  of  a  millionth 
part  of  their  whole  amount.  The  more  recently  discovered 
planets,  Uranus  and  Neptune,  will,  in  the  course  of  time, 
have  their  periods  determined  with  equal  precision.  Then, 
if  we  square  the  periods  expressed  in  years  and  decimals  of 
a  year,  and  extract  the  cube  root  of  this  square,  we  have 
the  mean  distance  of  the  planet  with  the  same  order  of 
precision. 

Again,  the  eccentricities  of  the  orbits  are  exactly  deter- 
mined by  careful  observations  of  the  positions  of  the  planets 
during  successive  revolutions.  Thus  we  can  draw  a  map 
of  the  planetary  orbits  so  exact  that  its  errors  will  entirely 
elude  the  most  careful  scrutiny,  though  the  map  itself 
might  be  many  yards  in  extent. 

On  such  a  map  we  can  lay  down  the  magnitudes  of  the 
planets  as  accurately  as  our  micrometers  can  measure 
their  angular  diameters.  Thus  we  know  that  the  mean 
diameter  of  the  Sun,  as  seen  from  the  earth,  subtends 
an  angle  of  32'.  We  can  therefore,  on  such  a  map  of  the 
solar  system,  lay  down  the  Sun  in  its  true  size,  on  the  scale 
of  the  map.  This  can  be  done  in  the  same  way  for  each 
of  the  planets,  the  Earth  and  Moon  excepted.  There  is  no 
immediate  and  direct  way  of  finding  how  large  the  Earth 
or  Moon  would  look  from  the  Sun  or  from  a  planet; 
whence  the  exception. 

But  without  further  research  we  shall  know  nothing 
about  the  scale  of  our  map.  That  is,  we  shall  have  no 
means  of  knowing  how  many  miles  in  space  correspond  to 
an  inch  on  the  map.  If  we  can  learn  either  the  distance 
or  magnitude  of  any  one  of  the  planets  laid  down  on  the 
map,  in  miles  or  in  semidiameters  of  the  Earth,  we  shall 
be  able  at  once  to  find  the  scale. 


262  ASTRONOMY. 

The  general  custom  of  astronomers  is  not  to  attempt  to 
use  a  scale  of  miles  at  all,  but  to  employ  the  mean  distance 
of  the  Sun  from  the  Earth  as  the  unit  in  celestial  measure- 
ments. Thus,  in  astronomical  language,  we  say  that  the 
distance  of  Mercury  from  the  Sun  is  0.387,  that  of  Venus 
0.723,  that  of  Mars  1.523,  that  of  Saturn  9.539,  and  so 
on  in  terms  of  the  Earth's  distance  =  1.000.  But  this 
gives  us  no  information  respecting  the  distances  in  terms 
of  terrestrial  measures. 

The  distance  of  the  Earth  in  miles  is  not  the  only 
unknown  quantity  on  our  map.  We  know  nothing  respect- 
ing the  distance  of  the  Moon  from  the  Earth,  because 
KEPLER'S  laws  apply  directly  to  bodies  moving  around  the 
Sun.  We  must  therefore  determine  the  distance  of  the 
Moon  as  well  as  that  of  the  Sun.  When  these  two  things 
are  done  a  map  of  the  solar  system  can  be  made  in  which 
every  measurement  can  be  expressed  in  miles. 

THE  SOLAR  AND  LUNAR  PARALLAX, 

The  problem  of  distances  in  the  solar  system  is  thus 
reduced  to  measuring  the  distances  of  the  Sun  and  Moon 
in  miles  or  in  terms  of  the  Earth's  radius  (=  4000  miles). 
The  most  direct  methods  of  doing  this  are  as  follows: 


FIG.  158. — DETERMINATION  OF  THE  DISTANCE  OF  TIRE  MOON. 


SOLAR   AND  LUNAR  PARALLAX  263 

Distance  of  the  Moon. — In  the  figure  C  is  the  centre  of 
the  Earth,  and  8'  and  8"  are  the  positions  of  two 
observers  on  its  surface.  P  is  the  Moon  in  space  and  PC 
is  the  distance  to  be  determined  (in  miles).  The  observer 
at  S"  sees  the  Moon  on  the  celestial  sphere  at  P" ,  and  he 
measures  its  zenith  distance  Z"P".  At  the  same  instant 
the  observer  at  8 '  sees  the  Moon  on  the  celestial  sphere  at 
P'  and  he  measures  its  zenith  distance  Z'P'.  (The  student 
must  imagine  the  circle  Z"  P"  to  be  completed,  and  Z'  a 
point  in  the  circle.)  Z"P"  and  Z'P'  are  then  known  arcs 
and  Z"S"P"  and  Z'8'P'  are  known  angles,  since  they  are 
measured  by  known  arcs.  The  angle  PS"Cis  known;  it 
is  180°  -  PS"Z".  The  angle  PS'C  is  known;  it  is 
180°  —  PS'Z'.  As  the  two  observers  are  at  stations  whose 
latitudes  are  known,  the  angle  S'CS"  is  known.  It  is  the 
difference  of  their  latitudes  (for  if  H'H^  is  the  plane  of  the 
Earth's  equator,  S^CH,  is  the  latitude  of  S"  and  S'CHV 
is  the  latitude  of  8'  and  therefore  S'CS"  is  known). 

In  the  quadrilateral  S'CS"P  the  three  angles  whose 
vertices  are  at  (7,  at  S',  and  at  S"  are  known,  and  therefore 
the  fourth  angle  whose  vertex  is  at  P  is  known.  In  this 
quadrilateral  two  of  the  sides  are  known  because  they  are 
radii  of  the  Earth.  Hence  the  distances  S'P  and  S"P 
are  known.  From  either  of  the  triangles  S'CP  or  8"CP 
the  distance  of  the  Moon,  CP,  can  be  calculated. 

This  is  one  method  of  determining  the  distance  of  the 
Moon.  Knowing  the  actual  dimensions  of  the  Earth  in 
miles,  observations  of  the  Moon  made  at  stations  widely 
separated  in  latitude,  as  Paris  and  the  Cape  of  Good  Hope, 
can  be  combined  so  as  to  give  the  Moon's  distance  in  miles. 
On  precisely  the  same  principles  the  distances  of  Venus  or 
Mars  have  been  determined  in  miles. 

The  Distance  of  the  Sun  from  Transits  of  Venus. — When 
Venus  is  at  inferior  conjunction  she  is  between  the  Sun 
and  the  Earth.  If  her  orbit  lay  in  the  ecliptic,  she  would 


264 


ASTRONOMY. 


be  projected  on  the  Sun's  disk  at  every  inferior  conjunc- 
tion. The  inclination  of  her  orbit  is,  in  fact,  about  3£°, 
and  thus  transits  of  Venus  occur  only  when  she  is  near  the 
node  of  her  orbit  at  the  time  of  inferior  conjunction.  In 
Fig.  159  let  E,  V,  8  be  the  Earth,  Venus,  and  the  Sun. 
DC  is  a  part  of  Venus1  orbit.  An  observer  at  B  will  see 
Venus  impinge  on  the  Sun's  disk  at  /,  be  just  internally 
tangent  at  //,  move  across  the  disk  to  ///,  and  off  at  IV. 


Fra.  159. — DETERMINATION  OF  THE  DISTANCE  OF  THE  SUN. 

Similar  phenomena  will  occur  for  A  at  1,  2,  3,  4.  When 
A  sees  Venus  at  «,  B  will  see  her  at  b.  ab  :  AB  : :  Va  :  VA ; 
but  VA  :  Va  as  1  :  2-J-  nearly,  ab  therefore  occupies  on 
the  Sun's  disk  a  space  2-^  times  as  large  as  the  Earth's 
diameter.  If  we  measure  the  angular  dimension  ab  in  any 

E 


FIG.  160. 


way,  and  divide  the  resulting  angle  by  2|,  we  shall  have 
the  angle  subtended  at  the  Sun  by  the  Earth's  diameter; 
or  if  we  divide  it  by  5,  the  angle  subtended  at  the  Sun 
by  the  Earth's  radius.  (Fig.  160.)  Having  this  angle 


MASSES  OF  THE  PLANETS.  265 

we  can  calculate  the  Earth's  distance  from  the  Sun  in 
miles  from  the  right  triangle  SEC,  where  8  is  the  Sun,  C 
the  Earth's  centre,  and  E  the  end  of  the  Earth's  radius. 

The  angular  space  ab  can  be  calculated  at  a  transit  of 
Venus,  when  we  know  the  length  of  the  chords  //,  ///, 
and  2,  3.  The  length  of  each  chord  is  known  by  observing 
the  interval  of  time  elapsed  from  phase  II  to  phase  ///. 

Other  Methods  of  Determining  Solar  Parallax, — The 
most  accurate  method  of  measuring  the  Sun's  distance 
depends  upon  a  knowledge  of  the  velocity  of  light.  The 
time  required  for  light  to  pass  from  the  Sun  to  the  Earth 
is  known  with  considerable  exactness,  being  very  nearly 
498  seconds.*  If  we  can  determine  experimentally  how 
many  miles  light  moves  in  a  second,  we  shall  at  once  have 
the  distance  of  the  Sun  in  miles  by  multiplying  that 
quantity  by  498.  The  velocity  of  light  is  about  186,330 
miles  per  second.  Multiplying  this  by  498,  we  obtain 
92,800,000  miles  for  the  distance  of  the  Sun.  The  time 
required  for  light  to  pass  from  the  Sun  to  the  Earth  is 
still  somewhat  uncertain,  but  this  value  of  the  Sun's 
distance  is  probably  the  best  yet  obtained. 

RELATIVE  MASSES  OF  THE  SUN  AND  PLANETS. 

In  estimating  the  masses  as  well  as  the  distances  of  celestial  bodies 
it  is  necessary  to  use  what  we  may  call  celestial  units;  that  is,  to  take 
the  mass  of  some  celestial  body  as  a  unit,  instead  of  any  multiple  of 
the  pound  or  kilogram.  The  reason  of  this  is  that  the  ratios  be- 
tween the  masses  of  the  planetary  system,  or,  what  is  the  same 
thing,  the  mass  of  each  body  in  terms  of  that  of  some  one  body  as 
the  unit,  can  be  determined  without  knowing  the  mass  of  any  one 
of  them  in  pounds  or  tons.  To  express  a  mass  in  kilograms  or 
other  terrestrial  units,  it  is  first  necessary  to  find  the  mass  of  the 
Earth  in  such  units,  as  already  explained.  This,  however,  is  entirely 
unnecessary  for  astronomical  purposes.  In  estimating  the  masses  of 

*  See  page  256. 


266  ASTRONOMY. 

the  individual  planets,  that  of  the  Sun  is  generally  taken  as  a  unit. 
The  planetary  masses  are  then  all  very  small  fractions. 

The  ma^s  of  the  Sun  being  1.00,  the  mass  of  Mercury  is 

Venus  is 
Earth  is 
Mars  is 
Jupiter  is 
Saturn  is 
Uranus  is 
Neptune  is 

The  mass  of  the  Earth  being  1,  the  mass  of  the  Moon  is  ¥]T. 

The  masses  of  the  planets  that  have  satellites  are  determined  by 
measuring  the  attraction  that  is  exerted  by  the  planet  on  the  satellite. 

If  the  distance  of  the  planet  from  the  Sun  (M}  is  R  and  its  peri- 
odic time  is  T,  and  if  the  planet  whose  mass  is  m  has  a  satellite  re- 
volving in  a  circular  orbit  whose  radius  is  r  in  a  time  t,  it  is  proved 
in  Mechanics  that 

#2    r3 
Jf:m  =  _:_, 

by  which  expression  we  can  determine  m,  the  mass  of  the  planet,  in 
fractions  of  the  Sun's  mass  M,  because  R,  T,  r,  t  are  known.  In  this 
way  the  masses  of  all  the  planets  that  are  attended  by  satellites  are 
calculated,  after  making  suitable  allowances  for  the  fact  that  the 
orbits  of  the  satellites  are  ellipses  and  not  circles. 

Mercury  and  Venus  have  no  satellites,  and  their  masses  are  calcu- 
lated by  determining  the  perturbations  that  they  cause  in  the  motions 
of  other  planets  (and  of  comets)  in  their  vicinity. 

The  angular  diameters  of  the  planets  are  measured  with  a  microm- 
eter attached  to  a  telescope.  The  result  is  expressed  in  seconds  of 
arc.  Knowing  the  distance  of  the  planet  in  miles,  the  diameter  can 
also  be  expressed  in  miles.  (See  page  144.) 

The  surface  of  a  planet  is  proportional  to  the  square,  and  its  vol- 
ume to  the  cube  of  its  diameter.  The  mass  of  a  planet  is  deduced  as 
above  described.  Its  density  is  obtained  by  dividing  its  mass  by  its 
volume. 

In  what  has  gone  before  the  methods  of  determining  the 
mass,  the  distance,  the  diameter,  the  orbit,  etc.,  of  each 
planet  have  been  described  with  more  or  less  fullness.  The 
fundamental  principles  of  the  methods  are  all  that  can  be 


CELESTIAL  MEASUREMENTS.  267 

given  here.  The  details  of  the  processes  of  observation 
are  explained  in  works  on  Practical  Astronomy.  The 
mathematical  forms  involved  are  treated  in  works  on 
Celestial  Mechanics.  It  will  at  least  be  obvions  to  the 
student  that  the  masses,  the  distances,  and  the  orbits  of 
the  planets  can  be  determined  in  the  ways  that  have  been 
explained,  though  he  will  not  know  the  details  of  the 
processes  actually  employed. 

The  results  that  have  been  obtained  are  given  in  two 
tables  printed  in  Chapter  XV.  These  two  tables  contain 
data  sufficient  to  enable  us  to  construct  the  map  of  the 
solar  system  that  was  spoken  of  on  page  261.  With  the 
numbers  there  set  down  a  plan  of  the  solar  system  can  be 
made  with  great  exactness.  The  orbit  of  each  planet  can 
be  drawn  in  its  true  shape  and  situation.  The  place  of 
each  planet  at  any  past  or  future  time  can  be  assigned. 
The  diameter  of  each  planet  can  be  marked  on  the  map  to 
the  proper  scale.  The  mass,  the  force  of  gravity  at  the 
surface,  the  volume,  the  density  of  each  planet  is  known. 
The  problems  that  were  attacked  by  PTOLEMY,  COPER- 
NICUS, KEPLER,  and  NEWTON  are  solved.  The  solar 
system  considered  as  a  collection  of  heavy  bodies  revolving 
in  space  under  the  law  of  gravitation  is  explained. 

In  order  to  complete  the  description  of  the  solar  system 
something  more  is  necessary.  We  desire  to  know  the 
topography,  the  meteorology,  the  physical  condition  of 
each  planet  just  as  we  know  the  topography,  the  climates, 
the  physics  of  our  own  Earth.  We  wish  to  know  the 
geology  and  the  chemistry  of  the  stars  just  as  we  know 
the  geology  and  the  chemistry  of  the  Earth.  The  science 
that  treats  of  the  physical  condition  of  the  Sun,  Moon, 
planets,  stars,  and  other  celestial  bodies  is  called  Astro- 
nomical Physics  or  Astro-physics.  The  methods  of  this 
science  are  the  methods  of  terrestrial  physics  extended  so 
as  to  deal  with  all  celestial  bodies.  A  description  of  the 


268  ASTRONOMY. 

physical  condition  of  the  heavenly  bodies  is  called  Descrip- 
tive Astronomy.  The  second  part  of  this  book  is  chiefly 
devoted  to  such  a  description,  which  it  is  necessary  to  give 
in  a  very  abbreviated  form.  The  student  can  supplement 
what  is  printed  here  by  consulting  articles  on  the  Sun, 
Moon,  and  planets,  etc.,  in  any  good  encyclopedia,  or  by 
reading  some  of  the  excellent  books  on  Popular  Astronomy 
written  by  Sir  ROBERT  BALL,  FLAMMARION,  PROCTOR,  and 
others. 

—  What  is  the  most  convenient  unit  of  length  in  tlie  description 
of  the  solar  system  ?  How  is  the  periodic-time  of  a  planet  deter- 
mined ?  Knowing  the  periodic-time,  how  do  you  obtain  its  mean- 
distance?  How  is  the  angular  diameter  of  a  planet  found  ?  Explain 
the  principle  by  which  the  distance  of  the  Moon  from  the  Earth  may 
be  determined.  Explain  how  the  distance  of  the  Sun  from  the  Earth 
is  found  from  Transits  of  Venus  over  the  Sun's  disk.  Explain  how 
the  Sun's  distance  can  be  found  when  we  know  the  velocity  of  light. 
What  is  the  most  convenient  unit  of  mass  in  the  description  of  the 
solar  system  ?  On  what  principle  are  the  masses  of  Mars,  Jupiter, 
etc.,  determined? — the  masses  of  Mercury  and  Venus  ?  When  the 
mass  and  the  volume  of  a  planet  is  known,  how  is  its  density 
obtained  ? 


#    / 

'  i1  tt 

**f  r 


v 


PART    II. 
THE  SOLAR  SYSTEM. 


CHAPTER  XV. 

THE   SOLAR   SYSTEM. 

30.  The  solar  system  consists  of  the  sun  as  a  central 
body,  around  which  revolve  the  major  and  minor  planets, 
with  their  satellites,  a  few  periodic  comets,  and  a  number 
of  meteor  swarms.  These  are  permanent  members  of  the 
system.  Other  comets  appear  from  time  to  time  and  make 
part  of  a  revolution  around  the  sun,  and  then  depart  into 
space  again,  thus  visiting  the  system  without  being  per- 
manent members  of  it. 

The  bodies  of  the  system  may  be  classified  as  follows: 

I.  The  central  body — the  Sun. 

II.  The  four  inner  planets — Mercury,  Venus,  the  Earth, 
Mars. 

III.  A   group   of  small   planets,    called  Asteroids,   re- 
volving outside  of  the  orbit  of  Mars. 

IV.  A  group  of  four   outer  planets — Jupiter,  Saturn, 
Uranus,  and  Neptune. 

V.  The  satellites,  or  secondary  bodies,  revolving  about 
the  planets,  their  primaries. 

VI.  A  number  of  comets  and  meteor  swarms  revolving 
in  very  eccentric  orbits  about  the  Sun. 

The   eight  planets  of   Groups  II  and   IV  are  classed 

269 


270 


ASTRONOMY. 


together  as  the  major  planets,  to  distinguish  them  from  the 
five  hundred  or  more  minor  planets  of  Group  III.  Mercury 
and  Venus  are  inferior  planets  ;  the  other  major  planets 
are  called  superior  planets. 


FIG  161. — PLAN  OF  THE  SOLAR  SYSTEM. 

Dimensions  of  the  Solar  System. — The  figure  gives  a  plan 
of  part  of  the  solar  system  as  it  would  appear  to  a  spectator 
immediately  above  or  below  the  plane  of  the  ecliptic.  It  is 
drawn  approximately  to  scale,  the  mean  distance  of  the 
Earth  (=1)  being  half  an  inch.  On  this  scale  the  mean 
distance  of  Saturn  would  be  4.77  inches,  of  Uranus  9.59 
inches,  of  Neptune  15.03  inches.  On  the  same  scale  the 


THE  SOLAR  SYSTEM.  271 

distance  of  the  nearest  fixed  star  would  be  over  one  and 
one  half  miles.  The  student  should  remember  that  the 
immense  spaces  between  the  planets  and  between  the  stars 
are  empty  except  for  a  few  comets  and  for  swarms  of 
meteors.  The  striking  fact  is  how  few  are  the  bodies  that 
circulate  in  these  immense  regions  of  space. 

The  arrangement  of  the  planets  and  satellites  is,  then- — 

The  Inner  Group.  Asteroids.  The  Outer  Group. 

Mercury.  ,          minor  r  Jupiter  and  5  satellites. 

Venus.  I  and    rokaW  !  Saturn  and  9  satellites. 

Earth  and  Moon.  n    pr°        y  j  Uranus  and  4  satellites. 

Mars  and  2  satellites.  J  I  Neptune  and  1  satellite. 

The  different  planets  are  at  very  different  distances  from 
the  Sun.  To  the  nearest  planets,  Mercury  and  Venus,  the 
Sun  appears  as  a  very  large  disk.  To  the  earth  the  Sun 
appears  as  a  disk  about  half  a  degree  in  diameter.  The 
amount  of  light  and  heat  received  from  the  Sun  by  any 

planet  varies  as  -5  where  r  is  the  planets'  distance.     The 

surface  of  the  circles  in  figure  162  also  vary  as  -2  and  hence 

the  surfaces  show  the  relative  amounts  of  light  and  heat 
received  by  the  planets  (Flora  and  Mnemosyne  are  two  of 
the  asteroids).  The  distance  of  Neptune  from  the  Sun  is 
eighty  times  that  of  Mercury  and  it  receives  only  -g-^-g-  part 
as  much  light  and  heat. 

To  avoid  repetitions,  the  elements  of  the  major  planets 
and  other  data  are  collected  into  the  following  tables,  to 
which  the  student  should  constantly  refer  in  his  reading. 
The  units  in  terms  of  which  the  various  quantities  are 
given  are  those  familiar  to  us,  as  miles,  days,  etc.,  yet  some 
of  the  distances,  etc.,  are  so  immensely  greater  than  any 
known  to  our  daily  experience  that  we  must  have  recourse 
to  illustrations  to  obtain  any  idea  of  them  at  all. 


272 


ASTRONONY. 


For  example,  the  distance  of  the  sun  is  said  to  be  about  93  million 
miles.  It  is  of  importance  that  some  idea  should  be  had  of  this  dis- 
tance, as  it  is  the  unit,  in  terms  of  which  not  only  the  distances  in 
the  solar  system  are  expressed,  but  also  distances  in  the  stellar 


FIG.  162. — THE  APPARENT  SIZE  OF  THE  SUN  AS  VIEWED  FROM 
THE  DIFFERENT  PLANETS. 

universe.  Thus  when  we  say  that  the  distance  of  the  nearest  star  is 
over  200,000  times  the  mean  distance  of  the  sun,  it  becomes 
necessary  to  see  if  some  conception  can  be  obtained  of  one  factor  in 
this. 

Of  the  abstract  number,  93,000,000,  we  have  no  idea.     It  is  far  too 


THE  SOLAR  SYSTEM.  273 

great  for  us  to  have  counted.  We  have  never  taken  in  at  one  view 
even  a  million  similar  discrete  objects.  The  largest  tree  has  less 
than  500,000  leaves.  To  count  from  1  to  200  requires,  with  very 
rapid  counting,  60  seconds.  Suppose  this  kept  up  for  a  day  without 
intermission  ;  at  the  end  we  should  have  counted  288,000,  which  is 
about  ff|g  of  93,000,000.  Hence  over  10  months'  uninterrupted 
counting  by  night  and  day  would  be  required  simply  to  enumerate 
the  number,  and  long  before  the  expiration  of  the  task  all  idea  of  it 
would  have  vanished. 

We  may  take  other  and  perhaps  more  striking  examples.  We 
know,  for  instance,  that  the  time  of  the  fastest  express-trains  between 
New  York  and  Chicago,  which  average  40  miles  per  hour,  is  about  a 
day.  Suppose  such  a  train  to  start  for  the  sun  and  to  continue  run- 
ning at  this  rapid  rate.  It  would  take  363  years  for  the  journey. 
Three  hundred  and  sixty- three  years  ago  there  was  not  a  European 
settlement  in  America. 

A  cannon-ball  moving  continuously  across  the  intervening  space 
at  its  highest  speed  would  require  about  eight  years  to  reach  the  sun. 
In  a  little  less  than  a  day  it  would  go  once  round  the  earth  if  its 
course  was  properly  curved.  To  reach  the  sun  it  would  have  to 
travel  for  eight  years  at  this  velocity.  The  report  of  the  cannon,  if 
it  could  be  conveyed  to  the  sun  with  the  velocity  of  sound  in  air, 
would  arrive  there  four  years  after  the  projectile.  Such  a  distance 
is  entirely  inconceivable,  and  yet  it  is  only  a  small  fraction  of  those 
with  which  astronomy  has  to  deal,  even  in  our  own  system.  The 
distance  of  Neptune  is  30  times  as  great. 

If  we  examine  the  dimensions  of  the  various  orbs,  we  meet  almost 
equally  inconceivable  numbers.  The  diameter  of  the  sun  is  866,400 
miles;  its  radius  is  but  433,200,  and  yet  this  is  nearly  twice  the 
mean  distance  of  the  moon  from  the  earth.  Try  to  conceive,  in 
looking  at  the  moon  in  a  clear  sky,  that  if  the  centre  of  the  sun  could 
be  placed  at  the  centre  of  the  earth,  the  moon  would  be  far  within 
the  sun's  surface. 

Or  again,  conceive  of  the  force  of  gravity  at  the  surface  of  the 
various  bodies  of  the  system.  At  the  sun  it  is  nearly  28  times  that 
known  to  us.  A  pendulum  beating  seconds  here  would,  if  transported 
to  the  sun,  vibrate  with  a  motion  more  rapid  than  that  of  a  watch- 
balance.  The  muscles  of  the  strongest  man  would  not  support  him 
erect  on  the  surface  of  a  planet  of  the  mass  of  the  sun  :  even  lying 
down  he  would  be  crushed  to  death  under  his  own  weight  of  more 
than  two  tons.  At  the  moon's  surface  the  weight  of  a  man  would  be 
about  one-sixth  of  his  weight  on  the  earth  (since  the  Moon's  mass  is 


274:  ASTRONOMY. 

about  one-sixth  of  the  Earth's),  and  his  muscular  force,  on  such  a 
planet,  would  enable  him  to  bound  along  with  leaps  of  30  feet  or 
more.  There  are,  of  course,  no  human  beings  on  the  sun  or  on  the 
moon.  One  of  these  bodies  is  too  hot,  the  other  too  cold,  to  support 
human  life.  We  may  by  these  illustrations  get  some  rough  idea  of 
the  meaning  of  the  numbers  in  these  tables,  and  of  the  incapability 
of  our  limited  powers  to  comprehend  the  true  dimensions  of  even  the 
solar  system.  When  we  come  to  a  description  of  the  stellar  uni- 
verse we  shall  meet  with  distances  and  dimensions  almost  infinitely 
larger. 

It  is  important  that  the  student  should  realize,  so  far  as 
he  can,  the  data  given  in  these  tables;  and  there  is  no 
better  way  to  do  this  than  to  make  drawings  to  scale  from 
the  numbers  there  set  down.  For  instance,  let  the  student 
draw  lines  to  represent  the  apparent  angular  diameters  of 
the  different  planets  as  seen  from  the  Earth  (Table  II)  on 
a  scale  of  one  inch  =  30",  and  then  draw  the  circles  corre- 
sponding to  these  diameters.  None  of  the  circles  for  the 
planets  will  be  more  than  two  and  a  half  inches  in  diam- 
eter; but  if  he  wishes  to  draw  a  circle  to  represent  the 
apparent  disk  of  the  Sun  on  this  scale  it  will  have  to  be 
over  five  feet  in  diameter.  If  a  diagram  of  this  sort  is 
actually  constructed  it  will  impress  the  student's  mind  far 
more  than  a  mere  reading  of  the  figures  of  the  table,  If 
he  makes  a  drawing,  to  scale,  of  the  system  of  Jupiter 's 
satellites  putting  in  the  data  of  Table  III  and  whatever 
else  he  can  find  in  Chapter  XVIII,  a  definite  idea  of  the 
arrangement  and  sizes  of  these  satellites  will  be  acquired 
and  it  will  not  soon  be  forgotten.  The  distances  of  the 
periodic  comets  given  in  Table  IV  should  be  platted  to 
scale  along  with  the  major  axes  of  the  Earth,  Mars, 
Jupiter,  Saturn,  Uranus,  and  Neptune. 

Similar  diagrams  of  the  inclinations  of  the  planetary 
orbits,  of  their  periodic  times,  volumes,  masses,  densities, 
etc.,  will  serve  to  impress  the  mind  with  the  resemblances 
and  with  the  differences  in  the  different  bodies  of  the 
system. 


THE  SOLAS  SYSTEM.  275 

The  mass  of  the  sun  is  far  greater  than  that  of  any  single  planet  in 
the  system,  or  indeed  than  the  combined  mass  of  all  of  them.  If  the 
mass  of  the  earth  is  represented  by  a  single  grain  of  wheat  the  mass 
of  the  Sun  will  be  represented  by  about  four  bushels  of  such  grains. 
It  is  a  remarkable  fact  that  the  mass  of  any  given  planet  exceeds  the 
sum  of  the  masses  of  all  the  planets  of  less  mass  than  itself. 

The  total  mass  of  the  asteroids,  like  their  number,  is  unknown,  but 
it  is  probably  less  than  one-thousandth  that  of  our  Earth.  The  Sun's 
mass  is  over  700  times  greater  than  that  of  all  the  other  bodies,  and  the 
fact  of  its  central  position  in  the  solar  system  is  thus  explained.  In 
fact,  the  centre  of  gravity  of  the  whole  solar  system  is  very  little  out- 
side the  body  of  the  Sun,  and  will  be  inside  of  it  when  Jupiter  and 
Saturn  are  in  opposite  directions  from  it  (when  their  celestial  longi- 
tudes differ  by  180°). 

There  are  very  few  persons  who  realize  in  any  vivid  way 
the  distances  and  dimensions  of  the  planets  of  the  solar 
system.  No  very  keen  realization  is  to  be  had  by  merely 
reading  the  figures  of  the  tables.  If  it  is  practicable  the 
student  should,  once  in  his  life,  make  a  plan  of  the  solar 
system  in  the  following  way.  If  a  whole  class  can  make 
the  experiment  in  company  it  will  be  an  advantage. 

From  the  Tables  I  and  II  it  should  first  be  proved  that  if  the  Sun 
were  two  feet  in  diameter  instead  of  866,400  miles  the  different 
planets  would  be  fairly  well  represented  in  bulk  as  follows  : 

Mercury  by  a  grain  of  mustard-seed,  Venus  by  a  very  small  green 
pea,  The  Earth  by  a  common -sized  green  pea,  Mars  by  the  head  of  a 
rather  large  pin,  Jupiter  by  a  ball  of  the  size  of  an  orange,  Saturn 
by  a  golf-ball,  Uranus  by  a  common  marble,  Neptune  by  a  rather 
larger  marble. 

The  scale  of  the  plan  of  the  solar  system  is  to  be  two  feet  —  870,- 
000  miles.  To  make  the  plan  a  level  road  about  2|  miles  long  is 
needed.  A  stake  should  be  driven  into  the  ground  to  represent  the 
place  of  the  Sun,  and  if  the  length  of  the  stake  above  ground  is  two 
feet  the  Sun's  diameter  will  be  represented  by  it. 

The  distances  of  the  planets  must  be  laid  off  on  the  same  scale  of 
two  feet  =  870,000  miles.  Steps  of  two  feet  long  will  serve  to 
measure  the  distances.  The  student  should  first  verify  the  following 
from  the  numbers  given  in  Table  I.  On  the  adopted  scale  the  dis- 
tance from  the  Sun  to  Mercury  is  82  steps  ;  from  Mercury  to  Venus 
is  60  steps  ;  from  Venus  to  the  Earth  is  73  steps  ;  from  the  Earth  to 


276 


ASTRONOMY. 


Mars  is  108  steps  ;  from  Mars  to  Jupiter  is  785  steps  ;  from  Jupiter 
to  Saturn  is  934  steps  ;  Saturn  to  Uranus  is  2,086  steps ;  and  from 
Uranus  to  Neptune  is  2,322  steps. 

With  these  distances  let  the  student  set  out  from  the  stake  that 
represents  the  Sun  and  deposit  the  models  of  the  different  planets  at 
their  proper  distances — Mercury  at  82  steps  from  the  stake,  Venus  at 
142  steps,  and  so  on  to  Neptune,  which  will  be  6,450  steps  away — 
nearly  2£  miles. 

A  marble  2£  miles  away  from  a  globe  2  feet  in  diameter  represents 
the  relation  in  distance  and  in  size  between  Neptune  and  the  Sun.  A 
few  other  globes,  all  very  small,  at  large  intervals,  represent  the 
major  planets  A  few  grains  of  sand  represent  the  asteroids.  The 
spaces  of  the  solar  system  between  the  planets  are  empty  except  for 
a  few  comets  and  meteor-swarms. 

On  the  scale  of  the  model  the  distance  of  the  nearest  fixed  star 
from  the  stake  that  represents  the  Sun  is  8,000  miles.  A  globe 
about  three  or  four  feet  in  diameter  at  Peking  might  stand  for  this 
star  if  the  model  of  the  solar  system  were  made  in  New  York.  A 
morning  spent  in  actually  making  such  a  model  of  the  solar  system 
will  not  be  wasted.  There  is  no  better  way  of  realizing  the  dimen- 
sions of  the  bodies  of  the  solar  system  and  the  immense  extent  of 
empty  space  between  them. 

TABLE  I. 

(APPROXIMATE)  ELEMENTS  OF  THE  ORBITS  OF  THE  EIGHT 
MAJOR  PLANETS. 


Mean  Distance 

<M 

«g 

13     .    „, 

from  Sun. 

o 
£> 

«-i  - 

N 

5 

a  • 

!« 

s  2 
'Sc-' 

ll! 

NAME. 

Mil- 

!p 

ll 

o.g 

"3  H. 

11 

§g 

£1 

JIM 

Astronom- 

lions 

§•£ 

'&'i 

•Si 

ia 

S^ 

»fa£| 

ical  Units. 

of 

go 

8* 

oH 

cJ 

5* 

££££ 

Miles. 

3 

g 

3" 

S 

P 

Mercury.. 

0.387099 

36.0 

0.21 

75° 

7°    0' 

47° 

323° 

0"     3ra 

Venus...  . 

0.723332 

67.2 

0.01 

129 

3    24 

75 

244 

0      6'j 

Earth... 

1.000000 

92.9 

0.02 

100 

0     0 

0 

100 

0      8 

Mars.   .  .  . 

1.523691 

141 

0.09 

333 

1    51 

48 

83 

0    13 

Jupiter  .  . 

5.202800 

483 

0.05 

12 

1    19 

99 

160 

0    43 

Saturn  .  . 

9.538861 

886 

0.06 

90 

2    29 

112 

15 

1    19 

Uranus  .  . 

19.18329 

1782 

0.05 

171 

0    46 

73 

29 

2    38 

Neptune.. 

30.05508 

2791 

0.01 

46 

1    47 

130 

335 

4      8 

THE  SOLAR  SYSTfiM. 


277 


.JL  O  $> 

i5-3  S 


I>        C?        QO 


T-l  O  <N  1-1 


O      02 


«l 


CO         CO 

o      d 


TH  O  TH  I—I 


»  a—a 

S.S    S 


o      o      o      o      o      o      o      o 


CJ         CO 

o 


IS     ^ 

11 


g  s  • !  I  •  a 

i   f  I  I 

a   5   c2   5 


278 


ASTRONOMY. 


- 


o  * 

II 5 


"•»  ««  >H    g«M 

co          O  i— i  £  O 


S  ^ 

1-2 

Cl  M 


£  Sc 

8-2 

S8 

0.2 


—  — 


m       DBS 


I11S 


J,  *:~s  fr,.,.8-, 


111 


t^-eoo      OOOOO 

- 


OOOOOOJQOO 

T-I»—  it—  1»—  ti—  (-Tf^i^O 


SJ|2 

•a  fe  P 


i  t-i       O»-i«C-?C          |  I-H-H  W  Tj<  10  j^  Ol       W^CXJCO 


!g^Is  Sil 


few 


ffi    s    ^ 


:  es  o     oi'S  «,:  :  :   '-2  2  :  '•!«. 

:lli  luifrlfi! 


'f-St>      "  N co  •* .« ?o  t- ao e»  ^-c  o» co  •* 


TEE  SOLAS  SYSTEM. 


279 


TABLE  IV. 
THE  COMETS  OP  THE  SOLAR  SYSTEM  (PERIODIC  COMETS). 


No. 

NAME. 

Time  of  Peri- 
helion Passage. 

r 

Perihelion 
Distance 
(approx.) 

11? 
Ill 

-sjQxS 

Inclination 
of  Orbit 
(approx.) 

1 

Encke  

1895  Feb      4 

3  30 

0  34 

4  10 

13° 

2 

Tempel  

1894  April  23 

5  22 

1  35 

4  67 

13° 

3 

Brorsen     

1890  Feb     24 

5  46 

0  59 

5.61 

29° 

4 

Ternpel  Swift  

1891  Nov    14 

5  53 

1  09 

5.17 

5° 

5 

^^innecke 

1892  June  30 

5  82 

0  89 

5  58 

15° 

6 

7 

Da  Vico-Swift  
Tern  pel   

1894  Oct.     12 
1885  Sept  25 

5.86 
6  51 

1.39 

2  07 

5.11 
4  90 

3° 

11° 

8 

Biela  

1852  Sept    — 

6  6- 

0  86 

6.2- 

13° 

9 

Finlay  

1893  July    12 

6  62 

0.99 

6.06 

3° 

10 

D'  Arrest  

1890  Sept.  17 

6.69 

1.32 

5.78 

16° 

11 

Wolf  .. 

1891  Sept     3 

6  82 

1  59 

5  60 

25° 

13 

Brooks     .... 

1896  Nov      4 

7  10 

1  96 

5  43 

6° 

18 

Fave.  . 

1881  Jan     22 

7  57 

1  74 

5.97 

12° 

14 

Tuttle  

1885  Sept    11 

13  76 

1.02 

10.46 

55° 

15 
16 

Pons-Brooks  . 
Olbers 

1884  Jan.    25 
1887  Oct        8 

71.48 
72  63 

0.76 
1  20 

33.6? 
83  6° 

74Q 

45* 

17 

Halley  

1835  Nov    15 

76  37 

0  59 

35  41 

162° 

CHAPTER  XVI. 

THE  SUN. 

31.  The  Sun  is  a  huge  globe  866,400  miles  in  diameter. 
Its  mass  is  333,470  times  that  of  the  Earth,  its  volume  is 
1,310,000  times  the  Earth's  volume,  its  density  one  fourth 
of  the  Earth's  density.  The  force  of  gravity  on  its  surface 
is  nearly  28  times  the  force  of  gravity  on  the  Earth.  On 
the  Earth  a  heavy  body  falls  16  feet  during  the  first  second 
of  its  descent;  at  the  San  it  would  fall  444  feet.  Some 
idea  of  its  enormous  size  can  be  had  by  remembering  that 
the  Earth  and  Moon  are  but  238,000  miles  apart  while  the 
Sun's  radius  is  433,200  miles.  If  the  San  were  hollow 
and  the  Earth  was  at  its  centre  the  Moon  would  revolve  far 
within  the  outer  shell  of  the  Sun's  surface.  The  motions 
of  all  the  planets  are  controlled  by  its  attraction. 

The  Sun  is  a  star.  It  is  a  sphere  of  incandescent  gases 
and  metallic  vapors.  It  shines  by  its  own  light  and  gives 
out  enormous  quantities  of  heat  unceasingly.  Only  the 
smallest  fraction  of  the  Sun's  heat  reaches  the  Earth.  Yet 
that  small  fraction  (about  ^oinroVFo  UT  Part)  supports  all  the 
life  on  the  Earth,  both  of  animals  and  plants.  It  main- 
tains the  circulation  of  winds,  of  ocean  currents,  the  flow 
of  glaciers  and  of  rivers;  it  is  the  cause  of  the  rains,  the 
clouds,  the  dews  that  support  vegetation;  it  controls  the 
seasons  and  the  climates  of  all  the  regions  of  our  globe  and 
of  all  the  planets  in  the  solar  system.  In  the  strictest  sense 
all  the  life,  energy,  and  activity  on  the  Earth  are  main- 
tained by  the  Sun  and  principally  and  chiefly  by  the  Sun's 

280 


THE  SUN.  281 

heat.  If  the  Sun's  heat  were  cut  off  all  life  on  the  Earth 
would  quickly  cease. 

While  it  is  true  that  the  Sun  is  as  different  as  possible 
from  the  Earth  in  its  present  state,  it  is  to  be  especially 
noted  that  the  difference  is  chiefly  due  to  a  difference  of 
temperature.  The  spectroscope  detects  the  presence  of 
(the  vapors  of)  metals  and  earths  in  the  Sun  and  it  is  likely 
that  there  is  no  "  element  "  on  the  Earth  that  is  not  found 
on  the  Sun.  Calcium,  carbon,  copper,  hydrogen,  iron, 
magnesium,  nickel,  silver,  sodium,  zinc,  among  others, 
have  been  detected,  some  of  them  in  great  abundance. 
There  is  every  reason  to  believe  that  if  the  Earth  were  to 
be  suddenly  raised  to  the  temperature  of  the  Sun  it  would 
become  at  once,  and  in  virtue  of  temperature  alone,  a  Sun 
— that  is  a  star. 

Photosphere, — The  visible  shining  surface  of  the  Sun  is 
called  the  photosphere,  to  distinguish  it  from  the  body  of 
the  Sun  as  a  whole.  The  apparently  flat  surface  presented 
by  a  view  of  the  photosphere  is  called  the  Sun's  disk. 

Spots. — When  the  photosphere  is  examined  with  a  tele- 
scope, dark  patches  of  varied  and  irregular  outline  are  fre- 
quently found  upon  it.  These  are  called  the  solar  spots. 

.Rotation. — When  the  spots  are  observed  from  day  to 
day,  they  are  found  to  move  over  the  Sun's  disk  from  east 
to  west  in  such  a  way  as  to  show  that  the  Sun  rotates  on 
its  axis  in  a  period  of  25  or  26  days.  The  Sun,  therefore, 
has  axis,  poles,  and  equator,  like  the  Earth,  the  axis  being 
the  line  around  which  it  rotates.  It  turns  on  its  axis  from 
west  to  east  in  25  days,  7  hours,  48  minutes. 

Faculae. — Groups  of  minute  specks  brighter  than  the 
general  surface  of  the  Sun  are  often  seen  in  the  neighbor- 
hood of  spots  or  elsewhere.  They  are  clouds  of  the  vapors 
of  metals  and  are  called  faculce. 

Chromosphere. — Just  above  the  solar  photosphere  there 
is  a  layer  of  glowing  vapors  and  gases  from  5000  to  10,000 


282  ASTRONOMY. 

miles  in  depth.  At  the  bottom  of  it  lie  the  vapors  of  many 
metals,  magnesium,  sodium,  iron,  etc.,  volatilized  by  the 
intense  heat,  while  the  upper  portions  are  composed  prin- 
cipally of  hydrogen  gas.  The  vaporous  atmosphere  is  called 
the  chromosphere.  It  is  entirely  invisible  to  direct  vision, 
whether  with  the  telescope  or  naked  eye,  except  for  a  few 
seconds  about  the  beginning  or  end  of  a  total  eclipse,  but  it 
may  be  seen  on  any  clear  day  through  the  spectroscope. 

Prominences,  Protuberances,  or  Red  Flames. — The  gases 
of  the  chromosphere  are  frequently  thrown  up  in  irregular 
masses  to  vast  heights  above  the  photosphere,  it  may  be 
50,000,  100,000,  or  even  200,000  kilometres  (120,000 
miles).  These  masses  can  never  be  directly  viewed  except 
when  the  sunlight  is  cut  off  by  the  intervention  of  the 
Moon  during  a  total  eclipse.  They  are  then  seen  as  rose- 
colored  flames,  or  piles  of  bright  red  clouds  of  irregular  and 
fantastic  shapes  rising  from  the  edge  of  the  Sun.  The 
spectroscope  shows  that  they  are  chiefly  composed  of  in- 
candescent calcium,  helium,  and  hydrogen. 

Corona. — During  total  eclipses  the  Sun  is  seen  to  be 

enveloped  by  a  mass  of  soft 
white  light,  much  fainter  than 
the  chromosphere,  and  extend- 
ing out  on  all  sides  far  beyond 
the  highest  prominences.  It 
is  brightest  around  the  edge 
of  the  Sun,  and  fades  off 

toward  its  outer  boundary  by 
FIG.   163.— A  METHOD  OF  OB-    .  .U1  -,   ,.  mi. 

SERVING  THE  SUN   WITH   A   ^sensible    gradations.      This 
TELESCOPE.  halo    of   lis^ht    is   called   the 

corona,  and  is  a  very  striking  object  during  a  total  eclipse. 
(Fig.  163.) 

Methods  of  Observing  the  Sun. — The  light  and  heat  of  the  Sun  con- 
centrated at  the  focus  of  a  telescope  are  very  intense.  An  experi- 
ment with  a  burning-glass  will  illustrate  this  obvious  fact.  Special 


THE  SUN.  283 

eye-pieces  are  made  so  that  the  Sun  can  be  looked  at  directly  with 
the  telescope,  but  the  method  of  projecting  the  Sun's  image  on  a 
sheet  of  cardboard  (as  in  the  figure)  is  very  convenient,  especially 
because  several  observers  can  examine  the  image  at  the  same  time. 
A  sheet  of  white  cardboard  is  fastened  to  the  telescope  (accurately 
perpendicular  to  its  axis)  by  a  light  wooden  or  metal  frame.  The 
image  of  the  Sun  is  projected  on  the  cardboard  and  must  be  made 
as  sharp  and  neatly  denned  as  possible  by  moving  the  eye  piece  to 
and  fro  till  the  right  focus  is  found.  It  is  desirable  to  fasten  another 
sheet  of  cardboard  over  the  tube  of  the  telescope  to  shut  off  a  part 
of  the  daylight,  as  in  the  figure. 


FIG.  164.— COPY  OF  A   PHOTOGRAPH  OP  THE  SUN  SHOWING  THE 
CENTRE  OF  THE  DISK  TO  BE  BRIGHTER  THAN  THE  EDGES. 

One  of  the  best  ways  to  study  the  Sun  is  to  photograph  it  with  a 
camera  of  long  focus— the  longer  the  better.  The  exposures  must 
be  very  short  indeed — a  few  thousandths  of  a  second  in  most  cases. 
The  surroundings  of  the  Sun — its  red  flames,  its  corona— can  be  seen 
with  the  naked  eye  at  a  total  solar  eclipse,  and  they  can  then  be 
photographed.  The  spectroscope  is  used  for  the  study  of  the  Sun's 
surroundings  and  of  its  surface,  as  explained  in  the  Appendix  on 
Spectrum  Analysis.  If  the  student  is  not  already  familiar  with  the 
subject  through  his  study  of  physics,  he  should  interrupt  his  read- 
ing of  this  chapter  and  master  the  principles  explained  in  the  Ap- 
pendix, as  they  are  necessary  to  an  understanding  of  what  follows. 


284 


The  Photosphere,  —  The  disk  of  the  San  is  circular  in 
shape,  no  matter  what  side  of  the  Sun's  globe  is  turned 
towards  the  Earth,  whence  it  follows  that  the  Sun  is  a 
sphere.  The  disk  of  the  San  is  not  equally  bright  over  all 
the  circle  of  the  surface.  The  centre  of  the  disk  is  most 
brilliant  and  the  edges  are  shaded  off  so  as  to  appear  much 
less  brilliant,  as  in  Fig.  164.  The  deficiency  of  brightness 
at  the  edges  is  due  to  the  fact  that  the  rays  that  reach  us 
from  the  centre  of  the  disk  traverse  a  smaller  depth  of  the 
Sun's  atmosphere  than  those  from  the  edges  and  are  less 
absorbed  by  the  Sun's  atmosphere  therefore. 


FIG 


165.  —  THE  ABSORPTION  OF  THE  SUN'S  RATS  is  GREATER  AT 
THE  EDGES  OP  THE  DISK  THAN  AT  THE  CENTRE. 


In  figure  165  let  8E  be  the  Sun's  radius  and  8M  the  radius  of  his 
atmosphere.  A  person  stationed  beyond  M  (to  the  left  hand  of  the 
figure)  looking  at  the  Sun  along  the  lines  ME  and  M'E'  would  see 
the  centre  of  the  disk  by  rays  that  had  traversed  the  distance  ME 
only;  while  the  edge  of  the  disk  would  be  seen  by  rays  that  had 
traversed  the  much  greater  distance  M'  E'. 


THE  SUN. 


285 


The  ray  which  leaves  the  centre  of  the  Sun's  disk  in  passing  to 
the  Earth  traverses  the  smallest  possible  thickness  of  the  solar 
atmosphere,  while  the  rays  from  points  of  the  Sun's  body  which 
appear  to  us  near  the  limbs  pass,  on  the  contrary,  through  the  maxi- 
mum thickness  of  atmosphere,  and  are  thus  longest  subjected  to  its 
absorptive  action. 

The  Solar  Spots, — When  the  Sim's  disk  is  examined  with 
the  telescope  several  Sun-spots  can  usually  be  seen.  The 
smallest  are  mere  black  dots  in  the  shining  surface  500 
miles  or  so  in  diameter.  The  largest  solar  spots  are 
thousands  of  miles  in  diameter  (100,000  miles  or  more). 


FIG.  166. — A  LARGE  SUN-SPOT  SEEN  IN  THE  TELESCOPE. 

Solar  spots  generally  have  a  black  central  nucleus  or 
umbra,  surrounded  by  a  border  or  penum bra,  intermediate 
in  shade  between  the  central  blackness  and  the  bright 
photosphere. 

The  first  printed  account  of  solar  spots  was  given  by 
FABRITIUS  in  1611,  and  GALILEO  in  the  same  year  (May, 
1611)  also  described  them,  GALILEO'S  observations  showed 


286  ASTRONOMY. 

them  to  belong  to  the  Sun  itself,  and  to  move  uniformly 
across  the  solar  disk  from  east  to  west.  A  spot  just  visible 
at  the  east  limb  of  the  Sun  on  any  one  day  travelled  slowly 
across  the  disk  for  12  or  13  days,  when  it  reached  the  west 
limb,  behind  which  it  disappeared.  After  about  the  same 
period,  it  reappeared  at  the  eastern  limb. 

The  spots  are  not  permanent  in  their  nature,  bat  dis- 
appear after  a  few  days,  weeks,  or  months  somewhat  as 
cyclonic  storms  in  the  Earth's  atmosphere  persist  for  hours 
or  days  and  then  are  dissipated.  But  so  long  as  the  spots 
last  they  move  regularly  from  east  to  west  on  the  Sun's  ap- 
parent disk,  making  one  complete  rotation  in  about  25  days. 
This  period  of  25  days  is  therefore  approximately  the  rota- 
tion period  of  the  Sun  itself. 

Spotted  Region. — It  is  found  that  the  spots  are  chiefly  confined  to 
two  zones,  one  in  each  hemisphere,  extending  from  about  10°  to  35° 
or  40°  of  heliographic  latitude.  In  the  polar  regions  spots  are 
scarcely  ever  seen,  and  on  the  solar  equator  they  are  much  more  rare 
than  in  latitudes  10°  north  or  south.  Connected  with  the  spots,  but 
lying  on  or  above  the  solar  surface,  are  faculce,  mottlings  of  light 
brighter  than  the  general  surface  of  the  Sun.  Many  of  the  faculce, 
are  clouds  of  incandescent  calcium. 

Solar  Axis  and  Equator. — The  spots  revolve  with  the  surface  of  the 
Sun  about  his  axis,  and  the  directions  of  their  motions  must  be  ap- 
proximately parallel  to  his  equator.  Fig.  167  shows  the  appearances  as 
actually  observed,  the  dotted  lines  representing  the  apparent  paths 
of  the  spots  across  the  Sun's  disk  at  different  times  of  the  year. 

In  June  and  December  these  paths,  to  an  observer  on  the  Earth, 
seem  to  be  right  lines,  and  hence  at  these  times  the  observer  must  be 
in  the  plane  of  the  solar  equator.  At  other  times  the  paths  are 
ellipses,  and  in  Marchand  September  the  planes  of  these  ellipses  are 
most  oblique,  showing  the  spectator  to  be  then  furthest  from  the 
plane  of  the  solar  equator.  The  inclination  of  the  solar  equator  to 
the  plane  of  the  ecliptic  is  about  7°  9',  and  the  axis  of  rotation  is,  of 
course,  perpendicular  to  it. 

Form  of  the  Solar  Spots.— The  Sun-spots  are  probably  depressions 
in  the  photosphere.  When  a  spot  is  first  seen  at  the  edge  of  the 
disk  it  appears  as  a  notch,  and  is  elliptical  in  shape.  As  the  Sun's 
rotation  carries  it  further  on  to  the  disk  it  becomes  more  and  more 


THE  SUN. 


287 


circular.  At  the  centre  it  is  often  circular,  and  as  it  passes  off  the 
disk  the  shape  again  becomes  elliptical.  The  appearances  are  shown 
in  fig.  168,  and  are  due  to  perspective. 


FIG  167.— APPARENT  PATHS  OF  THE  SOLAR  SPOTS  TO  AN  OBSERVED 
ON  THE  EAKTH  AT  DIFFERENT  SEASONS  OF  THE  YEAR. 

The  Number  of  Solar  Spots  varies  Periodically. — The 
number  of  solar  spots  that  are  visible  varies  from  year  to 
year.  Although  at  first  sight  this  might  seem  to  be  what 
we  call  a  purely  accidental  circumstance,  like  the  occur- 
rence of  cloudy  and  clear  years  on  the  Earth,  observations 
of  sun-spots  establish  the  fact  that  this  number  varies 
periodically. 


288 


ASTRONOMY. 


That  the  solar  spots  vary  periodically  will  appear  from  the  follow- 
ing summary  : 

From  1828  to  1831  the  Sun  was  without  spots  on  only       1  day. 
In  1833 

From  1836  to  1840 
In  1843 

From  1847  to  1851 
In  1856 

From  1858  to  1861 
In  186! 


FIG.   168.— APPEARANCE  OF  THE  SAME  SOLAR  SPOT  NEAR  THE 
CENTRE  OF  THE  SUN  AND  NEAR  THE  EDGE. 

Every  eleven  years  there  is  a  minimum  number  of  spots,  and  about 
five  years  after  each  minimum  there  is  a  maximum.  There  was  a 
maximum  of  spots  in  1893  ;  the  minimum  occurred  in  1899.  If,  in- 
stead of  merely  counting  the  number  of  spots,  measurements  are 
made  on  solar  photographs  of  the  extent  of  spotted  area,  the  period 
comes  out  with  greater  distinctness. 

The  cause  of  this  periodicity  is  as  yet  unknown.  It  probably  lies 
within  the  Sun  itself,  and  is  similar  to  the  cause  of  the  periodic  ac- 
tion of  a  geyser. 

The  sudden  outbreak  of  a  spot  on  the  Sun  is  often  accompanied  by 
violent  disturbances  in  the  magnetic  needle  ;  and  there  is  a  complete 


THE  SUN.  289 

concordance  between  certain  changes  in  the  magnetic  declination 
and  the  changes  in  the  Sun's  spotted  area. 

The  agreement  is  so  close  that  it  is  now  possible  to  say  what  the 
changes  in  the  magnetic  needle  have  been  so  soon  as  we  know  what 
the  variations  in  the  Sun's  spotted  area  are. 

There  is  a  direct  action  between  the  Sun  and  the  Earth  that  we 
call  their  mutual  gravitation  ;  and  the  foregoing  facts  show  that 
they  influence  each  other  in  yet  another  way.  These  actions  take 
place  across  the  space  of  93,000,000  miles  which  separates  the  Sun 
and  Earth.  No  doubt  a  similar  effect  is  felt  on  every  planet  of  the 
solar  system. 

The  Sun's  Chromosphere  and  Corona.  Phenomena  of  Total  Eclipses. 
When  a  total  solar  eclipse  is  ob- 
served with  the  naked  eye  its 
beginning  is  marked  simply  by 
the  small  black  notch  made  in 
the  luminous  disk  of  the  Sun  by 
the  advancing  edge  or  limb  of 
the  Moon.  This  always  occurs 
on  the  western  half  of  the  Sun, 
because  the  Moon  moves  from 
west  to  east  in  its  orbit.  An 
hour  or  more  elapses  before  the 
Moon  has  advanced  sufficiently 
far  in  its  orbit  to  cover  the  Sun's 
disk.  During  this  time  the  disk 
of  the  Sun  is  gradually  hidden 
until  it  becomes  a  thin  crescent. 

The  actual  amount  of  the  Sun's 
light  may  be  diminished  to  two   T 
thirds    or   three    fourths   of   its  FlG'    169-~THE   SOLAR    CORONA 

,.  .  .  AT  THE  TOTAL  SOLAR  ECLIPSE 

ordinary     amount     without     its       op  JANUARY,   i889>  FROM  PHO. 

being    strikingly    perceptible  to       TOGRAPHS. 
the  eye.     What  is  first  noticed  is 

the  change  which  takes  place  in  the  color  of  the  surrounding  land- 
scape, which  begins  to  wear  a  ruddy  aspect.  This  grows  more  and 
more  pronounced,  and  gives  to  the  adjacent  country  that  weird  effect 
which  lends  so  much  to  the  impressiveness  of  a  total  eclipse. 

The  reason  for  the  change  of  color  is  simple.  The  Sun's  atmos- 
phere absorbs  a  large  proportion  of  the  bluer  rays,  and  as  this 
absorption  is  dependent  on  the  thickness  of  the  solar  atmosphere 
through  which  the  rays  must  pass,  it  is  plain  that  just  before  the 
Sun  is  totally  covered,  the  rays  by  which  we  see  it  will  be  redder 


290  ASTRONOMY. 

than  ordinary  sunlight,  as  they  are  those  which  come  from  points 
near  the  Sun's  limb,  where  they  have  to  pass  through  the  greatest 
thickness  of  the  Sun's  atmosphere. 

The  color  of  the  light  becomes  more  and  more  lurid  up  to  the  mo- 
ment of  total  eclipse.  If  the  spectator  is  upon  the  top  of  a  high 
mountain,  he  can  then  begin  to  see  the  Moon's  shadow  rushing  to- 
ward him  at  the  rate  of  a  kilometre  in  about  a  second.  Just  as  the 
shadow  reaches  him  there  is  a  sudden  increase  of  darkness  ;  the 
brighter  stars  begin  to  shine  in  the  dark  lurid  sky,  the  thin  crescent 
of  the  Sun  breaks  up  into  small  points  or  dots  of  light,  which  sud- 
denly disappear,  and  the  Moon  itself,  an  intensely  black  ball,  appears 
to  hang  isolated  in  the  heavens. 

An  instant  afterward  the  corona  is  seen  surrounding  the  black 
disk  of  the  Moon  with  a  soft  effulgence  quite  different  from  any 
other  light  known  to  us.  Near  the  Moon's  edge  it  is  intensely  bright, 
and  to  the  naked  eye  uniform  in  structure  ;  5'  or  10'  from  the  limb 
this  inner  corona  has  a  boundary  more  or  less  denned,  and  from  this 
extend  streamers  and  wings  of  fainter  and  more  nebulous  light. 
They  are  of  various  shapes,  sizes,  and  brilliancy.  No  two  solar 
eclipses  yet  observed  have  been  alike  in  this  respect. 

Superposed  upon  these  wings  may  be  seen  (sometimes  with  the 
naked  eye)  the  red  flames  or  protuberances  which  were  first  discov- 
ered during  a  solar  eclipse.  They  need  not  be  more  closely  de- 
scribed here,  as  they  can  now  be  studied  at  any  time  by  aid  of  the 
spectroscope. 

The  total  phase  lasts  for  a  few  minutes,  and  during  this  time,  as 
the  eye  becomes  more  and  more  accustomed  to  the  faint  light,  the 
outer  corona  becomes  visible  further  and  further  away  from  the 
Sun's  limb.  At  the  eclipse  of  1878,  July  29th,  it  was  seen  to  extend 
more  than  6°  (about  9,000,000  miles)  from  the  Sun's  limb.  Photo- 
graphs of  the  corona  show  even  a  greater  extension.  Just  before 
the  end  of  the  total  phase  there  is  a  sudden  increase  of  the  brightness 
of  the  sky,  due  to  the  increased  illumination  of  the  Earth's  atmos- 
phere near  the  observer,  and  in  a  moment  more  the  Sun's  rays  are 
again  visible,  seemingly  as  bright  as  ever.  From  the  end  of  totality 
till  the  last  contact  the  phenomena  of  the  first  half  of  the  eclipse  are 
repeated  in  inverse  order.* 

Telescopic  Aspect  of  the  Corona. — Such  are  the  appearances  to  the 

*  The  Total  Solar  Eclipse  of  May  28,  1900,  will  be  visible  in  the  United  States. 
Its  track  will  pass  from  New  Orleans  to  Norfolk  in  Virginia.  The  duration  of 
the  total  phase  will  be  about  1m.  19s.  in  Louisiana  and  1m.  49s.  in  North  Car- 
olina. The  totality  occurs  about  7.30  A.M.  (local  time)  at  New  Orleans,  and 
about  9  A.M.  at  Norfolk.  The  width  of  the  shadow  track  is  about  55  miles. 


THE  SUN.  291 

naked  eye.  The  corona,  as  seen  through  a  telescope,  is,  however, 
of  a  very  complicated  structure.  It  is  best  studied  on  photographs, 
several  of  which  can  be  taken  during  the  total  phase,  to  be  subse- 
quently examined  at  leisure. 

The  corona  and  red  prominences  are  solar  appendages.  It  was 
formerly  doubtful  whether  the  corona  was  an  atmosphere  belonging 
to  the  Sun  or  to  the  Moon.  At  the  eclipse  of  1860  it  was  proved  by 
measurements  that  the  red  prominences  belonged  to  the  Sun  and  not 
to  the  Moon,  since  the  Moon  gradually  covered  them  by  its  motion, 
they  remaining  attached  to  the  Sun.  The  corona  is  also  a  solar  ap- 
pendage. 

Gaseous  Nature  of  the  Prominences. — The  eclipse  of  1868  was  total 
in  India,  and  was  observed  by  many  skilled  astronomers.  A  discov- 
ery of  M.  JANSSEN'S  will  make  this  eclipse  forever  memorable.  He 
was  provided  with  a  spectroscope,  and  by  it  observed  the  promi- 
nences. One  prominence  in  particular  was  of  vast  size,  and  when 
the  spectroscope  was  turned  upon  it,  its  spectrum  was  discontinuous, 
showing  the  bright  lines  of  hydrogen  gas. 

The  brightness  of  the  spectrum  was  so  marked  that  JANSSEN  de- 
termined to  keep  his  spectroscope  fixed  upon  it  even  after  the  reap- 
pearance of  sunlight,  to  see  how  long  it  could  be  followed.  It  was 
found  that  its  spectrum  could  be  seen  perfectly  well  after  the  return 
of  complete  sunlight  ;  and  that  the  prominences  could  be  observed  at 
any  time  by  taking  suitable  precautions. 

One  great  difficulty  was  conquered  in  an  instant.  The  red  flames 
which  formerly  were  only  to  be  seen  for  a  few  moments  during  total 
eclipses,  and  whose  observation  demanded  long  and  expensive 
journeys  to  distant  parts  of  the  world,  could  now  be  regularly 
ob-erved  with  all  the  facilities  offered  by  a  fixed  observatory. 

This  great  step  in  advance  was  independently  made  by  Sir  NOR- 
MAN  LOCKYER,  and  his  discovery  was  derived  from  pure  theory,  un- 
aided by  observations  of  the  eclipse  itself.  The  prominences  are 
now  carefully  mapped  day  by  day  all  around  the  Sun,  and  it  has 
been  proved  that  around  this  body  there  is  a  vast  atmosphere  of 
hydrogen  gas— the  chromosphere  From  this  the  prominences  are 
projected  sometimes  to  heights  of  100,000  miles  or  more. 

Spectrum  of  the  Corona. — The  spectrum  of  the  corona  was  first  ob- 
served by  two  American  astronomers— Professors  YOUNG  and  HARK- 
NESS— at  the  total  solar  eclipse  of  1869.  Since  that  time  it  has  been 
regularly  observed  at  every  total  eclipse  and  often  photographed. 
Expeditions  are  sent  to  observe  all  total  eclipses,  no  matter  in  what 
parts  of  the  Earth  they  occur,  as  up  to  the  present  time  there  is  no 
other  way  of  investigating  the  corona  and  its  spectrum. 


292  ASTRONOMY. 

The  spectrum  of  the  corona  consists  of  several  bright  lines  super- 
posed on  a  faint  continuous  band.  The  continuous  spectrum  is 
probably  due  to  sunlight  reflected  from  the  particles  (like  fog  or  dust 
particles)  present  in  the  corona.  The  bright  lines  prove  that  the 
corona  is  chiefly  made  up  of  self-luminous  gases  and  vapors. 


FIG.   170.— FORMS  OF  THE  SOLAR  PROMINENCES  AS  SEEN   WITH 
THE  SPECTROSCOPE. 

The  corona  is  a  mass  of  inconceivably  rarefied  matter 
enveloping  the  San  and  extending  far  out  into  space.  It 
is  excessively  rarefied,  as  is  proved  by  the  fact  that  comets 
moving  round  the  Sun  close  to  it  (and  thus  passing  through 
the  corona)  are  not  appreciably  retarded  -in  their  motions. 
The  gas  of  which  it  is  chiefly  made  up  has,  so  far,  not  been 
discovered  on  the  Earth. 

The  Sun's  Light  and  Heat. — The  light  of  the  Sun 
received  at  the  Earth  can  be  compared  with  our  gas-jets  or 
electric  lights.  Our  ordinary  gas-burners  or  electric  lights 
have  from  ten  to  twenty  "  candle-power."  The  quantity 
of  sunlight  is  1,575,000,000,000,000,000,000,000,000  times 
as  great  as  the  light  of  a  standard  candle.  The  Sun  sends 


THE  SUN.  293 

us  618,000  times  as  much  light  as  the  full  Moon,  and 
about  7,000,000,000  times  as  much  light  as  the  brightest 
star — Sirius. 

Amount  of  Heat  Emitted  by  the  Sun. — Owing  to  the 
absorption  of  the  solar  atmosphere,  we  receive  only  a  por- 
tion— perhaps  a  very  small  portion — of  the  rays  emitted  by 
the  Sun's  photosphere. 

If  the  Sun  had  no  absorptive  atmosphere,  it  would  seem 
to  us  hotter,  brighter,  and  more  blue  in  color,  since  the  blue 
end  of  the  spectrum  is  absorbed  proportionally  more  than 
the  red  end. 

The  amount  of  this  absorption  is  a  practical  question  to 
us  on  the  Earth.  So  long  as  the  central  body  of  the  Sun 
continues  to  emit  the  same  quantity  of  rays,  it  is  plain  that 
the  thickness  of  the  solar  atmosphere  determines  the  num- 
ber of  such  rays  reaching  the  Earth.  If  in  former  times 
this  atmosphere  was  much  thicker,  as  it  may  have  been, 
less  heat  would  have  reached  the  Earth.  Glacial  epochs 
may,  perhaps,  be  explained  in  this  way.  If  the  Sun  has 
had  different  emissive  powers  at  different  times,  as  it  may 
have  had,  this  again  would  have  produced  variations  in  the 
temperature  of  the  Earth  in  past  times. 

Amount  of  Heat  Eadiated. — There  is  at  present  no  way  of  determin- 
ing accurately  either  the  absolute  amount  of  heat  emitted  from  the 
central  body  or  the  amount  of  this  heat  stopped  by  the  solar  atmos- 
phere itself.  All  that  can  be  done  is  to  measure  the  amount  of  heat 
actually  received  by  the  Earth. 

Experiments  upon  this  question  lead  to  the  conclusion  that  if  our 
own  atmosphere  were  removed,  the  solar  rays  would  have  energy 
enough  to  melt  a  layer  of  ice  170  feet  thick  over  the  whole  Earth 
each  year. 

This  action  is  constantly  at  work  over  the  whole  of  the  Sun's  sur- 
face. To  produce  a  similar  effect  by  the  combustion  of  coal  at  the 
Sun  would  require  that  a  layer  of  coal  nearly  20  feet  thick  spread 
all  over  the  Sun's  surface  should  be  consumed  every  hour.  If  the 
Sun  were  of  solid  coal  and  produced  its  own  heat  by  combustion  alone 
it  would  burn  out  in  5000  yeais. 


294  ASTRONOMY. 

Of  the  total  amount  of  heat  radiated  by  the  Sun  the  Earth  receives 
but  an  insignificant  share.  The  Sun  is  capable  of  heating  the  entire 
surface  of  a  sphere  whose  radius  is  the  Earth's  mean  distance,  to  the 
same  degree  that  the  Earth  is  now  heated.  The  surface  of  such  a 
sphere  is  2,170,000,000  times  greater  than  the  angular  dimensions  of 
the  Earth  as  seen  from  the  Sun,  and  hence  the  Earth  receives  less 
than  one  two-billionth  part  of  the  solar  radiation. 

We  have  expressed  the  energy  of  the  Sun's  heat  in  terms  of  the  ice 
it  would  melt  daily  on  the  Earth.  If  we  compute  how  much  coal  it 
would  require  to  melt  the  same  amount,  and  then  further  calculate 
how  much  work  this  coal  would  do  if  it  were  used  to  drive  a  steam- 
engine  for  instance,  we  shall  find  that  the  Sun  sends  to  the  Earth  an 
amount  of  heat  which  is  equivalent  to  one  horse-power  continuously 
acting  day  and  night  for  every  25  square  feet  of  the  Earth's  surface. 
Most  of  this  heat  is  expended  in  maintaining  the  Earth's  tempera- 
ture ;  but  a  small  portion,  about  y^,  is  stored  away  by  animals  and 
vegetables. 

Solar  Temperature. — From  the  amount  of  heat  actually  radiated  by 
the  Sun,  attempts  have  been  made  to  determine  the  actual  tempera- 
ture of  the  solar  surface.  The  estimates  reached  by  various  authori- 
ties differ  widely,  as  the  laws  that  govern  the  absorption  within 
the  solar  envelope  are  almost  unknown.  Some  law  of  absorption  has 
to  be  assumed  in  any  such  investigation,  and  the  estimates  have  dif- 
fered widely  according  to  the  adopted  law. 

Professor  YOUNG  states  this  temperature  at  about  18,000°  Fahr. 
According  to  all  sound  philosophy,  the  temperature  of  the  Sun  must 
far  exceed  any  terrestrial  temperature.  There  can  be  no  doubt  that  if 
the  temperature  of  the  Earth's  surface  were  suddenly  raised  to  that 
of  the  Sun,  no  single  chemical  element  would  remain  in  its  present 
condition.  The  most  refractory  materials  would  be  at  once  volatilized. 

We  may  concentrate  the  heat  received  upon  several  square  feet 
(the  surface  of  a  huge  burning-lens  or  mirror,  for  instance),  examine 
its  effects  at  the  focus,  and,  making  allowance  for  the  condensation 
by  the  lens,  see  what  is  the  minimum  possible  temperature  of  the 
Sun.  The  temperature  at  the  focus  of  the  lens  cannot  be  higher  than 
that  of  the  source  of  heat  in  the  Sun  ;  we  can  only  concentrate  the 
heat  received  on  the  surface  of  the  lens  to  one  point  and  examine  its 
effects.  No  heat  is  created  by  the  lens. 

If  a  lens  three  feet  in  diameter  be  used,  the  most  refractory  mate- 
rials, as  fire-clay,  platinum,  the  diamond,  are  at  once  melted  or  volatil- 
ized. The  effect  of  the  lens  is  plainly  the  same  as  if  the  Earth  were 
brought  closer  to  the  Sun,  in  the  ratio  of  the  diameter  of  the  focal 
image  to  that  of  the  lens.  In  the  case  of  the  lens  of  three  feet,  al- 


THE  SUN.  295 

lowing  for  the  absorption,  etc.,  this  distance  is  yet  greater  than  that 
of  the  Moon  from  the  Earth ,  so  that  it  appears  that  any  comet  or 
planet  so  close  as  240,000  miles  to  the  Sun  must  be  vaporized  if  com- 
posed of  materials  similar  to  those  in  the  Earth. 

How  is  the  Sun's  Heat  Maintained  ? — It  is  certain  that 
the  Sun's  heat  is  not  kept  np  by  combustion.  If  the  Sun 
were  entirely  composed  of  pure  coal  its  combustion  would 
not  serve  to  maintain  the  Sun's  supply  of  heat  for  more 
than  5000  years.  We  know  that  the  Earth  has  been  in- 
habited by  people  of  high  civilization  (in  Egypt  for  example) 
for  a  much  longer  time  than  this.  Moreover  the  Sun 
cannot  be  a  huge  mass  once  very  hot  and  now  cooling 
because  there  has  certainly  been  no  great  diminution  of 
terrestrial  temperatures  in  the  past  3000  years,  as  is  shown 
by  what  is  known  of  the  history  of  the  vine,  the  fig,  etc. 
A  body  freely  cooling  in  space  would  lose  its  heat 
rapidly. 

There  are  two  explanations  that  deserve  mention.  The  first  is 
that  the  Sun's  heat  is  maintained  by  the  constant  falling  of  meteors 
on  its  surface.  It  is  well  known  that  great  amounts  of  heat  and 
light  are  produced  by  the  collision  of  two  rapidly  moving  heavy 
bodies,  or  even  by  the  passage  of  a  heavy  body  like  a  meteorite 
through  the  atmosphere  of  the  Earth.  In  fart,  if  we  had  a  certain 
mass  available  with  which  to  produce  heat  by  burning,  it  can  be 
shown  that,  by  burning  it  at  the  surface  of  the  Sun,  we  should  pro- 
duce  less  heat  than  if  we  simply  allowed  it  to  fall  into  the  Sun.  If 
it  fell  from  the  Earth's  distance,  it  would  give  6000  times  more  heat 
by  its  fall  than  by  its  burning. 

The  least  velocity  with  which  a  body  from  space  can  fall  upon 
the  Sun's  surface  is  about  280  miles  in  a  second  of  time,  and  the 
velocity  may  be  as  great  as  350  miles. 

No  doubt  immense  numbers  of  meteorites  do  fall  into  the  Sun 
daily  and  hourly,  and  to  each  one  of  them  a  certain  considerable  por- 
tion of  heat  is  due.  It  is  found  that  to  account  for  the  present 
amount  of  radiation  meteorites  equal  in  mass  to  the  whole  Earth 
would  have  to  fall  into  the  Sun  every  century.  It  is  in  the  highest 
degree  improbable  that  a  mass  so  large  as  this  is  added  to  the  Sun  in 
this  way  per  century,  because  the  Earth  itself  and  every  other  planet 


296  ASTRONOMY. 

would  receive  far  more  than  its  present  share  of  meteorites,  and 
would  become  quite  hot  from  this  cause  alone. 

The  meteoric  theory  deserves  a  mention,  but  it  is  probably  not  a 
sufficient  explanation. 

There  is  still  another  way  of  accounting  for  the  Sun's  constant 
supply  of  energy,  and  this  has  the  advantage  of  appealing  to  no 
cause  outside  of  the  San  itself  in  the  explanation.  It  is  by  suppos- 
ing the  heat,  light,  etc.,  to  be  generated  by  a  constant  and  gradual 
contraction  of  the  dimensions  of  the  solar  sphere.  As  the  globe  cools 
by  radiation  into  space,  it  must  shrink.  As  it  shrinks,  heat  is  pro- 
duced and  given  out. 

When  a  particle  of  the  Sun  moves  towards  the  Sun's  centre  the 
same  amount  of  heat  is  produced  if  its  motion  is  caused  by  a  slow 
shrinking  as  would  be  developed  by  its  sudden  fall  through  the  same 
distance. 

This  theory  is  in  complete  agreement  with  the  known  laws  of 
force.  It  also  admits  of  precise  comparison  with  facts,  since  the 
laws  of  heat  enable  us,  from  the  known  amount  of  heat  radiated,  to 
infer  the  exact  amount  of  contraction  in  inches  which  the  linear  di- 
mensions of  the  Sun  must  undergo  in  order  that  this  supply  of  heat 
may  be  kept  unchanged,  as  it  is  practically  found  to  be. 

With  the  present  size  of  the  Sun,  it  is  found  that  it  is  only  neces- 
sary to  suppose  that  its  diameter  is  diminishing  at  the  rate  of  about 
250  feet  per  year,  or  4  miles  per  century,  in  order  that  the  supply  of 
heat  radiated  shall  be  constant.  Such  a  change  as  this  may  be  taking 
place,  since  we  possess  no  instruments  sufficiently  delicate  to  have 
detected  a  change  of  even  ten  times  this  amount  since  the  invention 
of  the  telescope. 

It  may  seem  a  paradoxical  conclusion  that  the  cooling  of  a  body 
may  cause  it  to  give  out  heat.  This  indeed  is  not  true  when  we 
suppose  the  body  to  be  solid  or  liquid.  It  is,  however,  proved  that 
this  law  holds  for  gaseous  masses— but  only  so  long  as  they  are  gas- 
eous. 

We  cannot  say  whether  the  Sun  has  yet  begun  to  liquefy  in  his 
interior  parts,  and  hence  it  is  impossible  to  predict  at  present  the 
duration  of  his  constant  radiation.  It  can  be  shown  that  after  about 
5,000,000  years,  if  the  Sun  radiates  heat  as  at  present,  and  still  re- 
mains  gaseous,  his  present  volume  will  be  reduced  to  one  half.  If 
the  volume  is  reduced  to  one  half  the  density  will  be  then  two  times 
greater  (since  the  mass  will  remain  the  same).  (D  =  M  ^  F,  see 
page  237.)  It  seems  probable  that  somewhere  about  this  time  the 
solidification  will  have  begun,  and  it  is  roughly  estimated,  from  this 


THE  SUN.  297 

line  of  argument,  that  the  present  conditions  of  heat  radiation 
cannot  last  greatly  over  10,000,000  years. 

The  future  of  the  Sun  (and  hence  of  the  Earth)  cannot,  as  we  see, 
be  traced  with  great  exactitude.  The  past  can  be  more  closely  fol- 
lowed if  we  assume  (which  is  tolerably  safe)  that  the  Sun  up  to  the 
present  has  been  a  gaseous  and  not  a  solid  or  liquid  mass.  Four 
hundred  years  ago,  then,  the  Sun  was  about  16  miles  greater  in 
diameter  than  now  ;  and  if  we  suppose  the  process  of  contraction  to 
have  regularly  gone  on  at  the  same  rate  (a  very  uncertain  supposi- 
tion), we  can  fix  a  date  when  the  Sun  filled  any  given  space,  out 
even  to  the  orbit  of  Neptune ;  that  is,  to  the  time  when  the  polar 
system  consisted  of  but  one  body,  and  that  a  gaseous  or  nebulous 
one. 

It  is  not  to  be  taken  for  granted,  however,  that  the  amount  of  heat 
to  be  derived  from  the  contraction  of  the  Sun's  dimensions  is  infinite, 
no  matter  how  large  the  primitive  dimensions  may  have  been.  A 
body  falling  from  any  distance  to  the  Sun  can  only  have  a  certain 
finite  velocity  depending  on  this  distance  and  upon  the  mass  of  the 
Sun  itself,  which,  even  if  the  fall  be  from  an  infinite  distance, 
cannot  exceed,  for  the  Sun,  350  miles  per  second.  In  the  same  way 
the  amount  of  heat  generated  by  the  contraction  of  the  Sun's 
volume  from  any  size  to  any  other  is  finite  and  not  infinite. 

It  has  been  shown  that  if  the  Sun  has  always  been 
radiating  heat  at  its  present  rate,  and  if  it  had  originally 
filled  all  space,  it  has  required  some  18,000,000  years  to 
contract  to  its  present  volume.  In  other  words,  assuming 
the  present  rate  of  radiation,  and  taking  the  most  favor- 
able case,  the  age  of  the  Sun  does  not  exceed  18,000,000 
years.  The  Earth  is,  of  course,  less  aged. 

The  supposition  lying  at  the  base  of  this  estimate  is  that 
the  radiation  of  the  Sun  has  been  constant  throughout  the 
whole  period.  This  is  quite  unlikely,  and  any  changes  in 
this  datum  will  affect  the  final  number  of  years  to  be 
assigned.  While  this  number  may  be  greatly  in  error,  yet 
the  method  of  obtaining  it  seems  to  be  satisfactory,  and 
the  main  conclusion  remains  that  the  past  of  the  Sun  is 
finite,  and  that  in  all  probability  its  future  is  a  limited  one. 

The  exact  number  of  centuries  that  it  is  to  last  are  of 


298  ASTRONOMY. 

no  especial  moment  even  were  the  data  at  hand  to  obtain 
them:  the  essential  point  is  that,  so  far  as  we  can  see,  the 
San,  and  incidentally  the  solar  system,  has  a  finite  past 
and  a  limited  future,  and  that,  like  other  natural  objects, 
it  passes  through  its  regular  stages  of  birth,  vigor,  decay, 
and  death,  in  one  order  of  progress. 


CHAPTER   XVII. 
THE  PLANETS  MERCURY,   VENUS,   MARS. 

32.  Mercury — Venus — Mars. — Mercury  is  the  nearest 
planet  to  the  Sun.  Its  mean  distance  is  36,000,000  miles, 
about  yVV  of  tne  Earth's  distance.  Its  orbit  is  quite 
eccentric,  so  that  its  maximum  distance  from  the  Sun  is 
43,500,000  miles,  and  its  minimum  only  28,500,000.  At 
its  mean  distance  (0.39)  it  would  receive  about  6T«7  times 
as  much  light  and  heat  from  the  Sun  as  the  Earth,  because 

(l.OO)2  :  (0.39)2  =  6.6  :  1.0. 

Its  sidereal  year  is  88  days.  Its  time  of  rotation  on  its  axis 
is  not  certainly  known,  but  the  observations  of  SCHIA- 
PAEELLI  and  others  make  it  likely  that  it  revolves  once  on 
its  axis  in  the  same  time  that  it  makes  one  revolution  about 
the  Sun,  just  as  our  own  Moon  revolves  once  on  its  axis 
during  one  of  its  revolutions  about  the  Earth.  The 
apparent  angular  diameter  of  Mercury  can  be  measured 
with  the  micrometer  (see  page  144).  Knowing  the  angle 
that  the  diameter  of  the  planet  subtends  and  knowing  the 
planet's  distance  (in  miles)  the  diameter  of  the  planet  in 
miles  can  be  calculated.  The  diameter  of  Mercury  is  about 
3000  miles.  Its  surface  is  %  of  the  Earth's  surface  and  its 
volume  about  -fa.  The  mass  of  the  planet  is  determined  by 
calculating  how  much  matter  it  must  contain  to  affect  the 
motions  of  comets  as  it  is  observed  to  do.  In  this  way  it 
results  that  its  mass  is  about  ^  of  the  Earth's  mass.  Its 
density  is  about  T\  of  the  Earth's  density. 

299 


300  ASTRONOMY. 

Venus'1  mean  distance  is  67,200,000  miles.  Its  sidereal 
year  is  225  days.  It  is  not  yet  certain  that  its  period  of 
rotation  may  not  be  about  24  hours — one  day,  bat  the 
observations  of  SCHIAPARELLI  and  others  make  it  likely 
that  its  rotation  on  its  axis  is  performed  in  225  days  also. 
If  this  be  so  Mercury  and  Venus  will  always  turn  the  same 
face  to  the  Sun,  just  as  our  Moon  always  turns  the  same 
face  to  the  Earth.  The  diameter  of  Venus  is  7700  miles, 
only  a  little  less  than  the  diameter  of  the  Earth  (7918)  and 
it  has  therefore  about  the  same  volume.  The  mass  of 
Venus  is  determined  by  calculating  how  much  matter  the 
planet  must  contain  in  order  to  affect  the  motion  of  the 
Earth  as  it  is  observed  to  do.  Its  mass  is  about  T8^  of  the 
Earth's  mass  and  its  density  about  T9^  that  of  the  Earth. 

Very  little  is  certainly  known  about  the  geography  of 
Mercury  and  of  Venus.  Mercury  is  never  seen  far  distant 
from  the  Sun  and  observations  of  the  planet  in  the  daytime 
are  unsatisfactory  because  the  heated  atmosphere  of  the 
Earth  is  usually  in  constant  motion  and  produces  an  effect 
on  telescopic  images  like  the  twinkling  of  stars  to  the  naked 
eye.  Venus  shows  only  faint  markings  on  her  surface. 

It  is  likely  that  Mercury  has  little  or  no  atmosphere ;  and 
it  is  certain  that  Venus  has  an  atmosphere  of  some  kind 
which  is,  in  all  probability,  extensive.  If  the  surface  of 
Venus  which  we  see  with  the  telescope  is  nothing  but  the 
outer  rim  of  its  envelope  of  clouds  we  know  nothing  of  the 
real  surface  of  the  planet.  Nothing  whatever  is  known  as 
to  whether  either  of  these  planets  is  inhabited;  and  very 
little  as  to  whether  either  of  them  is  habitable. 

Apparent  Diameters  of  Mercury  and  Venus. — In  Fig.  171  S  is  the 
Sun,  E  the  Earth  in  its  orbit  and  LIMC  the  orbit  of  an  inferior 
planet.  If  the  Earth  is  at  E  and  the  planet  at  /,  the  planet  is  at 
inferior  conjunction  (nearest  the  Earth) ;  if  at  C,  at  superior  conjunc- 
tion ;  if  at  L  or  Mt  at  elongation.  The  Sun  will  be  seen  from  E  along 
the  line  EC.  It  is  plain  that  the  planet  can  never  appear  at  a  greater 
angle  from  the  Sun  than  SEM  or  8EL.  It  is  clear  from  the  figure 


THE  PLANETS  MERCURY  AND  VENU8. 


301 


that  the  apparent  angular  diameter  of  the  inferior  planet  will  vary 
greatly.  It  will  be  greatest  when  the  planet  is  nearest  the  Earth 
(inferior  conjunction)  and  least  when  the  planet  is  most  distant. 


FIG.  171  —THE  MOTION  OP  AN  INFERIOR  PLANET  WITH  REFER- 
ENCE TO  THE  EARTH. 


In  representing  the  apparent  angular  magnitude  of  these  planets, 
in  Figs.  172  and  178  we  suppose  their  whole  disks  to  be  visible,  as 
they  would  be  if  they  shone  by  their  own  light.  But  since  they  can 
be  seen  only  by  the  reflected  light  of  the  Sun,  those  portions  of  the 
disk  are  alone  seen  which  are  at  the 
same  time  visible  from  the  Sun  and  from 
the  Earth.  A  very  little  consideration 
will  show  that  the  proportion  of  the 
disk  which  can  be  seen  by  us  constantly 
diminishes  as  the  planet  approaches 
the  Earth,  and  that  the  planet's  di- 
ameter subtends  a  larger  angle.  FIG-  172.  -  APPARENT  Di- 

AMETER  OF  MERCURY  J   A  , 


Phase,  of  Mercury  and  Venus. 

When  the  planet  is  at  its  greatest  C,  AT  LEAST  DISTANCE. 
distance,  or  in  superior  conjunction  ((7,  Fig.  171),  its 
whole  illuminated  hemisphere  can  be  seen  from  the  Earth. 
As  it  moves  around  and  approaches  the  Earth,  the  illumi- 
nated hemisphere  is  gradually  turned  from  us.  At  the 
point  of  greatest  elongation,  M  or  Z,  one  half  the  hemi- 


302 


ASTRONOMY. 


sphere  is  visible,  and  the  planet  has  the  form  of  the  Moon 
at  first  or  second  quarter.  As  it  approaches  inferior  con- 
junction, the  apparent  visible  disk  assumes  the  form  of 
a  crescent,  which  becomes  thinner  and  thinner  as  the 
planet  approaches  the  Sun.  (See  Fig.  174.) 


FIG.  173.— APPARENT   DIAMETEU  OF  VENUS;  A,  AT   GREATEST  ; 
B,  AT  MEAN  ;  G,  AT  LEAST  DISTANCE. 

The  phases  of  an  inferior  planet  were  first  observed  by 
GALILEO  in  1610.  They  are  not  visible  to  the  naked  eye 
and  hence  their  discovery  dates  from  the  invention  of  the 


cc 


H 


FIG.  174. — PHASES  PRESENTED  BY  AN  INFERIOR  PLANET  AT  DIF- 
FERENT POINTS  OF  ITS  ORBIT;  K.  NEAR  INFERIOR — A, 
NEAR  SUPERIOR  CONJUNCTION. 

telescope.  If  the  student  will  turn  to  the  plan  of  the 
Ptolemaic  system  (Fig.  124)  he  will  see  that  PTOLEMY 
supposed  both  Mercury  and  Venus  to  revolve  about  the 


THE  PLANETS  MERCURY,   VENUS,  MARS.         303 

Earth  and  to  be  nearer  to  the  Earth  than  the  Sun.  There 
was  no  time,  according  to  PTOLEMY'S  system,  when  the 
whole  disk  of  Mercury  or  Venus  could  be  seen  illuminated. 
But  GALILEO'S  telescope  showed  the  disk  as  a  full  circle  at 
every  superior  conjunction.  The  inference  that  the 
Ptolemaic  system  was  not  true  was  irresistible.  The  failure 
of  PTOLEMY'S  theory  cleared  the  way  for  the  adoption  of 
the  heliocentric  theory  of  COPERNICUS. 

Transits  of  Mercury  and  Venus. — When  Mercury  or  Venus  passes 
between  the  Earth  and  Sun,  so  as  to  appear  projected  on  the  Sun's 
disk  as  a  dark  circle  the  phenomenon  is  called  a  transit.  If  these 
planets  moved  around  the  Sun  exactly  in  the  plane  of  the  ecliptic,  it 
is  evident  that  there  would  be  a  transit  at  every  inferior  conjunction, 
but  their  orbits  are  inclined  to  the  ecliptic  by  angles  of  7°  and  3°  re- 
spectively. 

The  longitude  of  the  descending  node  of  Mercury  at  the  present 
time  is  227°,  and  therefore  that  of  the  ascending  node  47°.  The 
Earth  has  these  longitudes  on  May  7th  and  November  9th.  Since  a 
transit  can  occur  only  within  a  few  degrees  of  a  node,  Mercury  can 
transit  only  within  a  few  days  of  these  epochs. 

The  longitude  of  the  descending  node  of  Venus  is  now  about  256° 
and  therefore  that  of  the  ascending  node  is  76°.  The  Earth  has  these 
longitudes  on  June  6th  and  December  7th  of  each  year.  Transits  of 
Venus  can  therefore  occur  only  within  two  or  three  days  of  these 
times.  (See  page  264.) 

Transits  of  Mercury  will  occur  in  1907,  1914  etc.,  and  of  Venus  in 
2004  and  2012. 

Mars  is  the  fourth  planet  in  order  going  outwards  from 
the  Sun.  Its  mean  distance  is  141,500,000  miles,  about  1£ 
times  the  Earth's  distance.  Its  orbit  is  quite  eccentric  so 
that  its  distance  from  the  Sun  at  diiferent  times  may  be  as 
large  as  153,000,000  or  as  small  as  128,000,000  miles.  Its 
distances  from  the  Earth  at  opposition  will  vary  in  the  same 
way.  When  its  distance  from  the  Sun  is  the  largest  the 
distance  from  the  Earth  will  be  about  60,000,000  miles 
(=  153,000,000  —  93,000,000).  When  its  distance  from 


304:  ASTRONOMY. 

the  Sun  is  the  smallest  the  distance  from  the  Earth  will  be 
about  35,000,000  miles  (=  128,000,000  —  93,000,000). 
When  Mars  is  in  conjunction  with  the  Sun  its  average 
distance  is  about  234,000,000  miles  (=  141,000,000  + 
93,000,000).  Its  greatest  distance  at  conjunction  is  about 
246,000,000  miles. 

The  apparent  angular  diameter  of  the  planet  varies  directly  as  the 
distance  and  is  sometimes  as  small  as  3". 6,  sometimes  seven  times 
larger  (246  -r-  35  =  7).  The  amount  of  light  received  by  Mars  from 

the  Sun  varies  as  -^  (where  R  =  Mars'  radius  vector),   so  that  the 

amount  of  light  received  by  the  Earth  from  Mars  varies  as  — — 

(where  r  is  the  distance  of  Mars  from  the  Earth).  The  amount  of 
light  icceived  by  us  from  the  planet  varies  enormously  at  different 
times,  therefore. 

The  periodic  time  of  Mars  is  687  days.  Its  diameter  is 
4200  miles — a  little  more  than  half  that  of  the  Earth.  Its 
surface  is  about  J  and  its  volume  is  ^  of  the  Earth's.  Its 
mass  is  determined  (by  calculating  the  effect  of  the  planet 
on  the  orbits  of  its  satellites)  to  be  about  J  of  the  Earth's 
mass.  Its  density  is  accurately  -ffc  of  the  Earth's  density, 
and  the  force  of  gravity  at  its  surface  is  about  T4¥  of  the 
Earth's.  A  body  weighing  100  pounds  on  the  Earth  would 
weigh  a  little  less  than  40  pounds  on  Mars. 

Mars  necessarily  exhibits  phases,  but  they  are  not  so  well 
marked  as  in  the  case  of  Venus,  because  the  hemisphere 
which  it  presents  to  the  observer  on  the  Earth  is  always 
more  than  half  illuminated.  The  greatest  phase  occurs 
when  its  direction  is  90°  from  that  of  the  Sun,  and  even 
then  six  sevenths  of  its  disk  is  illuminated,  like  that  of  the 
Moon,  three  days  before  or  after  full  moon.  The  phases 
of  Mars  were  observed  by  GALILEO  in  1610. 

Mars  has  little  or  no  Atmosphere. — The  Moon  reflects  ^  of  the 
light  falling  upon  it — about  as  much  as  sandstone  rocks.  Mercury 
reflects  I1$j.  These  bodies  have  little  or  no  atmosphere.  Venus  re- 


THE  PLANET  MAES.  305 

fleets  (from  the  outer  surface  of  its  envelope  of  clouds)  ^  of  tlie  in- 
cident light.  Jupiter  (T6^),  Saturn  (£&),  Uranus  (T«n%),  Neptune 
(T^),  are  all  bodies  surrounded  by  extensive  atmospheres  and  all  of 
them  have  high  reflecting  powers.  The  corresponding  number  for 
Mars  (y2^)  is  so  small  as  to  indicate  that  this  planet  has  little  atmos- 
phere, if  any. 

The  planet's  surface  has  been  under  careful  scrutiny  for 
many  years  and  observers  are  all  but  unanimous  in  their 
report  that  no  clouds  are  visible  over  the  surface. 

The  centres  of  the  disks  of  bodies  with  extensive  atmos- 
pheres (the  Sun,  Jupiter,  Saturn,  etc.)  are  always  brighter 
than  the  edges  (see  page  283).  The  centre  of  the  Moon, 
which  has  no  atmosphere,  is  not  so  bright  as  the  edge. 
Mars  is  like  the  Moon  in  this  respect  and  not  like  Jupiter. 
Finally  the  only  satisfactory  spectroscopic  observations  of 
the  planet  (made  independently  at  the  Lick  Observatory 
by  CAMPBELL  and  at  the  Allegheny  Observatory  by 
KEELER)  show  no  evidence  whatever  of  an  atmosphere  to 
Mars  and  no  sign  of  water-vapor  about  the  planet.  If 
there  is  any  atmosphere  at  all  it  can  hardly  be  more  dense 
than  the  Earth's  atmosphere  at  the  high  summits  of  the 
Himalaya  mountains — not  enough  to  support  human  life 
therefore.  As  there  is  no  evidence  of  the  presence  of 
water- vapor  and  of  clouds,  etc.,  it  follows  that  there  is 
little  or  no  water  on  the  planet's  surface.  The  spectrum 
of  Mars  and  the  spectrum  of  the  Moon  are  identical  in 
every  respect.  This  could  not  be  true  if  Mars  had  any 
considerable  atmosphere. 

It  is  proper  to  say  that  a  number  of  astronomers  hold  different 
views  and  that  popular  writers  on  astronomy,  with  few  exceptions, 
proclaim  the  existence  of  water,  air,  vegetation  and  intelligent  human 
beings  on  the  planet.  It  is  an  announcement  that  finds  thousands  of 
interested  listeners  who  are  only  too  glad  to  welcome  so  momentous 
a  conclusion.  The  popular  writings  referred  to  have  little  weight  in 
themselves,  but  they  have  undoubtedly  spread  a  general  belief  among 
intelligent  people  that  Mars  is  a  planet  much  like  the  Earth  (which 
it  certainly  is  not),  fit  for  human  habitation,  and  very  likely  inhabited 


306  ASTRONOMY. 

by  beings  like  ourselves.  The  questions  involved  are  inexpressibly 
important  in  themselves  and  they  relate  to  matters  in  which  every 
human  being  is  interested.  The  duty  of  Science  is  to  investigate  them 
by  every  possible  means  (and  this  has  been  and  will  be  done),  but 
Science  can  only  be  discredited  by  premature  and  incorrect  announce- 
ments made  without  a  proper  sense  of  responsibility. 


FIG.  175.— TELESCOPIC  VIEW  OF  THE  SURFACE  OF  MARS  SHOW- 
ING A  SMALL  "POLAR  CAP." 

The  important  and  long -continued  observations  of  SCHIAPARELLI 
on  Mars  led  him  to  announce  that  the  planet  was  provided  with  an 
elaborate  system  of  water-courses  ("oceans,  seas,  lakes,  canals,  etc."), 
and  the  authority  of  this  distinguished  observer  is  the  chief  support 
of  those  who  maintain  that  this  planet  is  fit  for  human  habitation, 
etc.  Complete  explanations  of  all  the  phenomena  presented  by  the 


THE  PLANET  MARS. 


307 


planet  cannot  be  given  in  the  light  of  our  present  knowledge. 
This  is  not  to  be  wondered  at  in  spite  of  the  industry  and  ability 
of  the  observers  who  have  spent  years  in  studying  the  planet.  The 
case  is  much  the  same  for  the  planets  Mercury,  Venus,  Jupiter,  Saturn, 
Uranus,  Neptune.  We  know  very  little  of  the  real  conditions  that 
prevail  on  their  surfaces.  We  know  comparatively  little  of  the  in- 
terior of  the  Earth  on  which  we  live  and  next  to  nothing  about  the 
interior  of  other  planets.  There  is  every  reason  to  believe  that 


FIG.  176.— DRAWING  OF  MARS  MADE  AT  THE  LICK  OBSERVATORY 
MAY  21,  1890. 

complete  explanations  will  be  forthcoming  in  time.  It  is,  at  any  rate, 
certain  that  the  conclusions  of  SCHIAPARELLI,  named  above,  cannot 
be  accepted  without  serious  modification,  as  will  be  shown  in  this 
Chapter. 

Appearance  of  the  Disk  of  Mars  in  the  Telescope. — The 
appearance  of  Mars  in  large  telescopes  is  shown  in  Figs. 
175  and  176.  The  main  body  of  the  planet  is  reddish 
(shown  white  in  the  cuts).  The  portions  shown  dark  in 


308  ASTRONOMY. 

the  pictures  are  bluish,  greenish,  or  grayish  in  the  tele- 
scope. The  "  cap  "  in  Fig.  175  is  a  brilliant  white.  Most 
of  the  markings  on  Mars  are  permanent.  They  are  seen 
in  the  same  places  year  after  year.  Observations  on  these 
permanent  markings  prove  that  the  planet  revolves  on  its 
axis  once  in  24h  37m  22s. 7.  Its  equator  is  inclined  to  the 
ecliptic  about  26°. 

When  Sir  WILLIAM  HERSCHEL  was  examining  Mars  in 
the  XVIII  century  he  called  the  red  areas  of  Mars  "  land  " 
and  the  greenish  and  bluish  areas  "  water."  It  was  a 
general  opinion  in  his  day  that  all  the  planets  were  created 
to  be  useful  to  man.  Astronomers  of  the  XVIII  century 
set  out  with  this  belief  very  much  as  the  philosophers  of 
PTOLEMY'S  time  set  out  with  the  fundamental  theorem  that 
the  Earth  was  the  centre  of  the  motions  of  the  planets. 
For  example,  HERSCHEL  maintained  that  the  Sun  was  cool 
and  habitable  underneath  its  envelope  of  fire.  He  says 
(1795)  "  The  Sun  appears  to  be  nothing  else  than  a  very 
eminent,  large  and  lucid  planet  .  .  .  most  probably  also 
inhabited  by  beings  whose  organs  are  adapted  to  the 
peculiar  circumstances  of  that  vast  globe."  It  is  certain 
that  the  Sun  is  not  inhabited  by  any  beings  with  organs. 
This  conclusion  is  now  as  obvious  as  that  no  beings 
inhabit  the  carbons  of  an  electric  street-lamp.  HERSCHEL'S 
guess  that  the  red  areas  on  Mars  were  "land  "  and  the 
blue  areas  "  water  "  had  no  more  foundation  than  his  guess 
that  the  Sun  might  be  inhabited. 

The  next  careful  studies  of  Mars  were  made  by  MAEDLER 
about  1840.  He  also  called  the  red  areas  of  the  disk 
"  land  "  and  the  dark  areas  "  water."  In  this  he  followed 
HERSCHEL.  There  was  no  reason  why  he  should  not  have 
called  the  red  areas  "  water  "  and  the  dark  areas  "  land." 
He  had  no  evidence  on  the  point.  The  same  is  true  of 
later  observers  down  to  the  first  observations  of  SCHIA- 
PARELH  about  1877, 


THE  PLANET  MARS.  309 

SCHIAPAKELLI  gave  reasons  for  these  names,  though  his 
reasons  are  not  convincing.  He  pointed  out  that  the 
narrow  dark  streaks  ("canals")  generally  ended  in  large- 
dark  areas  ("  oceans  ")  or  in  smaller  dark  areas  ("  lakes  "). 
The  narrow  dark  streaks  (very  seldom  less  than  60  miles 
wide)  are  quite  straight.  They  cannot  be  "  rivers"  then. 
If  they  are  water  at  all  the  name  "  canal  "  is  not  inappro- 
priate though  60  or  100  miles  is  a  very  wide  canal.  If  they 
are  water,  then  the  large  dark  areas  must  be  "  seas."  The 
narrow  dark  streaks  are  not  water,  however,  because  it  was 
discovered  by  Dr.  SCHAEBERLE  at  the  Lick  Observatory 
that  the  so-called  "seas"  sometimes  had  so-called 
"canals"  crossing  them.  A  "sea"  traversed  by  a 
"  canal "  is  an  absurdity.  If  it  could  be  imagined  it 
would  prove  the  "  inhabitants  "  and  the  "  engineers  "  of 
Mars  to  be  the  exact  reverse  of  "  intelligent."  It  is  main- 
tained by  some  recent  observers  of  Mars  that  some  of  the 
dark  areas  are  water  and  some  are  not  so.  The  bluish- 
green  color  of  the  dark  spots  is  said  to  "  suggest  vege- 
tation." But  who  can  know  what  colors  the  vegetation 
on  Mars  may  have  ? 

The  foregoing  very  brief  abstract  proves  that  the  dark 
areas  on  Mars  are  not  "  water."  The  red  areas  are  not 
known  to  be  "land."  The  spectroscopic  and  other  evi- 
dence proves  that  Mars  has  little  or  no  atmosphere — little 
or  no  water-vapor — no  clouds.  It  is  not  yet  known  what 
the  real  nature  of  the  red  areas  and  of  the  dark  areas  is. 
It  is  one  of  the  many  unsolved  problems  of  Astronomy  to 
discover  the  answer  to  this  fundamental  question.  There  is 
no  doubt  the  red  areas  and  the  large  dark  areas  have  a  real 
existence,  since  some  of  the  markings  on  Mars  have  been 
seen  for  more  than  two  centuries. 

It  is  not  certain  that  all  the  "canals  "  that  have  been  mapped  really 
exist.  Some  of  them  are  probably  mere  optical  illusions.  If  they 
were  real  streaks  on  the  planet's  surface  (like  wide  fissures,  broad 


310  ASTRONOMY. 

watercourses,  etc.)  they  would  always  appear  broadest  when  they 
were  at  the  centre  of  the  disk  and  would  always  be  narrower  when 
they  were  at  the  edges.  The  laws  of  perspective  demand  this.  It  is 
found  by  observation  that  the  reverse  is  frequently  true. 

SCHIAPARELLI  was  the  first  to  observe  that  many  of  the  "  canals" 
oftentimes  appear  to  be  doubled.  That  is,  a  canal  running  in  a  certain 
direction  which  generally  appeared  single,  thus, 


at  certain  times  was  no  longer  single  but  attended  by  a  companion, 
thus: 


Marvels  of  ingenious  speculation  have  been  printed  to  explain  why 
"intelligent  inhabitants"  having  one  "canal"  not  sufficient  for 
"commerce,"  did  not  widen  it,  but  preferred  to  dig  another  parallel 
to  it,  and  why  this  second  "canal  "  sometimes  vanished  altogether  in 
"  a  few  hours."  Recent  experiments  have  proved  that  these  com- 
panion canals  are  optical  illusions  produced  by  fatigue  of  the  eye  and 
by  bad  focusing.  Some,  at  least,  of  the  single  narrow  dark  streaks 
("canals")  have  a  real  existence.  It  is  probable  that  many  of  those 
laid  down  and  named  on  the  maps  of  SCHIAPARELLI,  LOWELL  and 
others  are  mere  illusions.  It  is  likely  that  all  the  double  canals 
were  so. 

Temperature  of  Mars. — The  distance  of  Mars  from  the 
Sun  is  1£  times  the  Earth's  distance.  The  heat  received 
by  the  Earth  from  the  Sun  is  to  the  heat  received  by  Mars 
as  (1.5)'J  =  2.25  to  1.  Mars  receives  less  than  one  half  as 
much  San  heat  as  the  Earth.  If  the  Earth  had  no  more 
atmosphere  than  the  Moon  the  Earth's  temperature  would 
be  like  that  of  the  Moon.  If  the  Earth  had  no  denser 
atmosphere  than  that  on  the  summits  of  the  Himalayas  the 
temperature  of  the  Earth  would  always  be  below  zero. 
Human  life  could  not  exist  here.  The  case  is  the  same 
with  Mars.  The  temperature  of  the  whole  surface  of  the 
planet  must  be  extremely  low — even  in  its  equatorial  regions. 
The  temperature  at  the  poles  of  Mars  must  be  several 
hundred  degrees  (Fahrenheit)  below  zero  when  the  pole  is 


THE  PLANET  MAES.  31 1 

turned  away  from  the  Sun  and  below  zero  even  when  the 
pole  is  turned  towards  the  Sun. 

Before  going  further  it  is  worth  while  to  consider  the 
circumstances  under  which  Mars  is  seen  by  an  observer  on 
the  Earth.  The  mean  distance  of  the  Moon  from  the 
Earth  is  240,000  miles.  If  it  is  viewed  through  a  field- 
glass  magnifying  4  times,  it  is  virtually  brought  within 
60,000  miles  of  the  observer  (240,000  -*-  4  =  60,000). 
The  nearest  approach  of  Mars  to  the  Earth  is  35,000,000 
miles.  The  planet  can  very  seldom  be  viewed  to  advantage 
with  a  magnifying  power  so  high  as  500.  If  such  a  power 
is  employed  when  Mars  is  nearest,  the  planet  is  virtually 
brought  within  70,000  miles  (35,000,000  -4-  500  =  70,000). 
It  follows  therefore  that  we  never  see  Mars  so  advan- 
tageously even  with  the  largest  telescopes  as  we  may  see  the 
Moon  in  a  common  field-glass.  If  the  student  will  ex- 
amine the  Moon  with  a  field-glass  magnifying  4  times  he 
will  have  a  realizing  sense  of  the  lest  conditions  under 
which  it  is  possible  to  see  Mars,  and  he  will  be  surprised 
that  so  much  is  known  of  the  planet.  The  industry  and 
fidelity  of  observers  can  only  be  appreciated  after  such 
an  experiment. 

The  Polar  Caps  of  Mars, — We  have  now  to  present 
another  result  of  observation  which  must  be  interpreted  in 
the  light  of  the  foregoing  facts — namely,  that  Mars  has 
little  or  no  water- vapor  and  that  its  temperature  is  appal- 
lingly low.  The  main  facts  of  observation  are  as  follows. 
CASSINI,  the  royal  astronomer  of  France,  discovered  in 
16(56  that  Mars  sometimes  had  dazzling  white  circular 
patches  near  his  poles  (see  Fig.  175).  In  1783  Sir 
WILLIAM  HERSCHEL  observed  these  patches  to  wax  and 
wane  and  he  called  them  "  snow  "  caps,  thus  begging  the 
question  as  to  their  real  nature.  HERSCHEL'S  observa- 
tions and  those  of  all  later  observers  show  that  these  caps 
wax  and  wane  with  the  Martian  seasons.  In  the  Martian 


ASTRONOMY. 

polar  summer  they  are  smallest,  or  they  even  vanish.  In 
the  Martian  polar  winter  they  are  largest.  As  HERSCHEL 
started  out  with  the  conviction  that  all  planets  were 
analogous  to  the  Earth  and  were  meant  to  be  inhabited, 
his  conclusion  was  that  the  polar  winter  condensed  water- 
vapor  into  snow  and  that  the  polar  summer  melted  this 
snow — and  so  on.  A  more  scientific  conclusion  would 
have  been  that  some  vapor  was  condensed  and  subsequently 
dissipated  by  the  solar  heat.  It  is  practically  certain  that 
the  phenomena  of  the  waxing  and  waning  of  the  caps 
depend  on  solar  heat. 

If  the  caps  are  "  snow  "  condensed  from  water- vapor  the 
layer  of  snow  must  be  exceedingly  thin,  because  when  these 
caps  are  "  melted  "  no  clouds  appear.  When  snow  melts 
on  the  Earth  clouds  are  formed  and  our  atmosphere  is 
charged  with  the  vapor  of  water.  No  clouds  are  seen  on 
Mars  and  no  water- vapor  is  to  be  found  above  its  surface 
by  any  spectroscopic  test. 

The  polar-caps  may  be  formed  by  the  vapor  of  some 
other  substance  than  water.  It  is  worth  while  to  inquire 
whether  they  may  not  be  carbon-dioxyd  in  a  solid  state. 
This  substance  is  a  heavy  gas  (carbonic-acid  gas)  at  ordi- 
nary temperatures.  It  would  lie  at  the  bottom  of  valleys 
and  fill  canons  or  ravines.  At  a  temperature  of  about  one 
hundred  Fahrenheit  below  zero  it  is  a  colorless  liquid.  At 
temperatures  such  as  must  obtain  at  the  pole  of  Mars 
turned  away  from  the  Sun  it  becomes  a  snow-like  solid. 
Caps  of  carbon-dioxyd  would  wax  and  wane  at  the  poles  of 
Mars  under  variations  of  solar  heat  such  as  obtain  at  these 
poles,  very  much  as  caps  af  snow  and  ice  wax  and  wane  in 
our  Arctic  regions  which,  under  all  circumstances,  are  at  a 
far  higher  temperature  than  the  poles  of  Mars. 

There  is  so  far  no  observational  proof  that  the  polar- 
caps  of  Mars  are  formed  of  carbon-dioxyd.  There  is 


THE  PLANET  MARS.  313 

convincing  proof  that  they  are  not  formed  of  water.  The 
question  as  to  the  nature  of  the  polar-caps  is  still  an  open 
one.  There  is  little  doubt  that  it  will,  one  day,  be  settled. 
The  scientific  attitude  of  mind  is  to  wait  for  proofs  of 
matters  still  unsolved;  to  accept  such  proofs  as  exist;  and 
to  eschew  unfounded  speculations.  All  that  is  now  known 
goes  to  show  that  Mars  has  little  or  no  atmosphere,  little 
or  no  water- vapor,  no  "  oceans,"  no  "  lakes, "no  "  canals," 
no  clouds.  Its  general  surface  is  rather  flat,  although 
a  few  mountain  chains  exist.  It  is  not  a  planet  like 
the  Earth.  It  is  much  more  like  the  Moon.  It  cannot 
possibly  be  "  inhabited  by  beings  like  ourselves." 

Satellites  of  Mars. — Until  the  year  1877  Marsw&s  supposed  to  have 
no  satellites.  But  in  August  of  that  year  Professor  HALL,  of  the 
Naval  Observatory,  instituted  a  systematic  search  with  the  great 
equatorial,  which  resulted  in  the  discovery  of  two  such  objects. 

These  satellites  are  by  far  the  smallest  celestial  bodies  known.  It 
is  of  course  impossible  to  measure  their  diameters,  as  they  appear  in 
the  telescope  only  as  points  of  light.  The  outer  satellite  is  probably 
about  six  miles  and  the  inner  one  about  seven  miles  in  diameter.  The 
outer  one  was  seen  with  the  telescope  at  a  distance  from  the  Earth  of 
7,000,000  times  this  diameter.  The  proportion  wo  -  Jd  be  that  of  a 
ball  two  inches  in  diameter  viewed  at  a  distance  equal  to  that  between 
the  cities  of  Boston  and  New  York.  Such  a  feat  of  telescopic  seeing 
is  well  fitted  to  give  an  idea  of  the  power  of  modern  optical  instru- 
ments in  detecting  faint  points  of  light  like  stars  or  satellites. 

The  outer  satellite,  called  Deimos,  revolves  around  the  planet  in 
30h  18™ ,  and  the  inner  one,  called  Phobos,  in  7h  39m.  The  latter  is 
only  5800  miles  from  the  centre  of  Mars,  and  less  than  4000  miles 
from  its  surface.  It  would  therefore  be  almost  possible  to  see  an 
object  the  size  of  a  large  animal  on  the  satellite  if  one  of  our  tele- 
scopes could  be  used  at  the  surface  of  Mars. 

The  short  distance  and  rapid  revolution  make  the  inner  satellite  of 
Mars  one  of  the  most  interesting  bodies  with  which  we  are  acquainted. 
It  performs  a  revolution  in  its  orbit  from  west  to  east  in  less  than 
half  the  time  that  Mars  revolves  on  its  axis.  In  consequence,  to  the 
inhabitant*  of  Mars  it  would  seem  to  rise  in  the  west  and  set  in  the  east. 


314 


ASTRONOMY. 


Let  the  student  prove  this  statement  for  himself  by  drawing  a 
figure  somewhat  like  Fig.  31.  Suppose  N  to  be  Mars,  a  the  spec- 
tator, ZH  the  celestial  equator,  Z  to  be  Phobos  on  the  meridian.  In 


FIG.  31  Us. 


lh  the  spectator  will  have  moved  to ;  and  Phobos  to ;  in  2h, 

etc.  etc. 

The  light  of  Phobos  is  about  -fa  of  the  light  of  our  Moon ;  of 
Deimos  about 


CHAPTER  XVIII. 

THE  MOON—  THE  MINOR  PLANETS. 

33,  The  Moon.  —  The  Moon  —  the  satellite  of  the  Earth  — 
revolves  about  its  primary  in  a  periodic-time  of  27d<32116 
at  a  mean  distance  of  238,840  miles.  Its  daily  motion 

360° 
among  the  stars  is  -^r^^rr^  ~  about  13°  11'.    The  apparent 


angular  diameter  of  the  Moon  is  about  half  a  degree,  so 
that  the  Moon  moves  daily  among  the  stars  about  26  of  its 
own  diameters.  The  interval  from  new  moon  to  new  moon 
is  about  29  days  and  the  Moon  comes  to  the  meridian  of 
an  observer  about  51  minutes  later  each  day  (on  the 
average).  The  orbit  of  the  Moon  is  inclined  to  the  plane 
of  the  ecliptic  by  a  little  more  than  5°. 

The  velocity  of  the  Moon  in  her  orbit  is  about  3350  feet 
per  second.  Her  diameter  is  2163  miles,  her  surface  T^g- 
of  the  Earth's,  her  volume  ^,  and  her  mass  -fa  of  the 
Earth's.  The  density  of  the  Moon  is  about  3.4  times  the 
density  of  water.  The  heaviest  lavas  of  the  Earth's  crust 
are  about  3.3  in  density,  so  that  the  conclusion  that  the 
Earth  and  Moon  once  formed  one  body  is  not  contradicted 
by  these  facts.  Gravity  on  the  Moon's  surface  is  J  as  great 
as  at  the  Earth's.  Hence  an  explosion  of  subterranean 
steam  would  form  a  much  more  extensive  crater  on  the 
Moon  than  on  the  Earth,  and  mountains  would  stand  at  a 
much  steeper  average  angle  on  the  Moon.  As  there  is  no 
air  and  no  water  on  the  Moon's  surface  there  is  no  frost 
constantly  working  to  overthrow  cliffs  and  sharp  peaks  as 

315 


316 


ASTRONOMY. 


FIG.  177. — LUNAR  LANDSCAPE  (Mare  Grisium)  FROM  PHOTOGRAPHS 
TAKEN  AT  THE  LICK  OBSERVATORY. 


THE  MOON.  317 


in  the  case  of  the  Earth.  The  albedo  of  the  Moon  is 
about  that  of  weathered  sandstone  rocks.*  The  angle  of 
slope  of  the  lunar  volcanoes  is  about  the  same  as  the  angle 
of  terrestrial  lavas.  These  and  many  other  facts  support 
the  conclusion  that  the  Earth  and  Moon  are  made  of  like 
materials. 

The  Moon  has  extremely  little  if  any  atmosphere 
because  the  occultation  of  a  star  by  the  lunar  disk  takes 
place  instantaneously.  If  the  Moon  had  an  atmosphere, 
the  star's  rays  would  be  refracted  by  it  and  there  would  be 
a  change  of  the  star's  color  and  a  gradual  disappearance. 
The  spectrum  of  the  Moon  is  nothing  but  a  fainter  solar 
spectrum.  This  proves  that  moonlight  is  reflected  sunlight; 
and  that  the  Moon  has  no  absorbing  atmosphere  of  its  own. 
No  doubt  the  Moon,  in  remote  past  times  had  an  atmos- 
phere. Its  constituents  have  probably  been  absorbed  by 
the  rocks  of  the  lunar  crust  as  they  cooled.  The  water  on 
the  Moon  has  probably  been  absorbed  in  the  same  way. 

The  quantity  of  light  received  by  the  Earth  from  the 
full  Moon  is  Tf-rsViro'  °f  the  light  received  from  the  Sun. 
The  temperature  of  the  Moon's  surface  is  probably  always 
below  freezing-point,  even  in  the  full  sunshine  of  a  long 
lunar  "day."  If  the  Earth's  atmosphere  were  to  be 
removed  the  temperature  of  our  summers  would  be  ex- 
tremely low  —  much  lower  than  it  now  is  at  the  summits  of 
our  highest  mountains.  The  lunar  "  night  "  is  14  terres- 
trial days  long.  The  temperature  of  a  part  of  the  Moon 
after  being  deprived  of  the  Sun's  light  (and  heat)  for  14 
days  must  be  extremely  low  —  several  hundred  degrees 
Fahr.  below  zero.f 

The  Moon  only  Shows  one  Face  to  the  Earth.—  The  Moon  rotates  on 
her  axis  from  west  to  east,  and  the  time  required  for  one  rotation  is  the 

*  The  albedo  of  any  substance  is  its  power  of  reflecting  rays  of 
light  that  fall  upon  it.  If  it  reflects  all  such  rays  its  albedo  is  100. 

f  These  are  the  conditions  that  prevail  on  airless  bodies  like  the 
Moon  and  Mars, 


318  ASTRONOMY. 

same  as  that  required  for  one  revolution  in  her  orbit,  viz.,  27  days. 
If  a  line  be  drawn  from  the  Earth  to  the  Moon  at  any  time  whatever 
this  line  will  always  touch  the  same  hemisphere  of  the  Moon :  and  the 
Moon  does  not  rotate  at  all  with  reference  to  this  line.  If  a  line  be 
drawn  through  the  Sun  parallel  to  the  Moon's  axis,  the  Moon  some- 
times turns  one  face  and  sometimes  another  to  this  line.  An  observer 
on  the  Earth  sees  but  one  hemisphere  of  the  moon.  An  observer 
on  the  Sun  would  successively  see  all  regions  of  the  Moon  (see  Fig. 
133). 

When  it  became  clearly  understood  after  the  invention  of 
the  telescope  that  the  ancient  notion  of  an  impassable  gulf 
between  the  character  of  "  bodies  celestial  and  bodies  terres- 
trial "  was  unfounded,  the  question  whether  the  Moon  was 
like  the  Earth  became  one  of  great  importance.  The  point 
of  most  especial  interest  was  whether  the  Moon  could,  like 
the  Earth,  be  peopled  by  intelligent  inhabitants.  Accord- 
ingly, when  the  telescope  was  invented  by  GALILEO,  one  of 
the  first  objects  examined  was  the  Moon.  With  every  im- 
provement of  the  instrument  the  examination  became  more 
thorough,  so  that  at  present  the  topography  of  the  Moon  is 
very  well  known.  Photographic  maps  of  the  Moon  show 
the  details  of  its  surface  in  an  admirable  way. 

With  every  improvement  in  the  means  of  research,  it  has 
become  more  and  more  evident  that  circumstances  at  the 
surface  of  the  Moon  are  totally  unlike  those  on  the  Earth. 
There  are  no  oceans,  seas,  rivers,  air,  clouds,  or  vapors. 
We  can  hardly  suppose  that  animal  or  vegetable  life  exists 
under  such  circumstances.  We  might  almost  as  well 
suppose  a  piece  of  granite  or  lava  to  be  the  abode  of  life  as 
the  surface  of  the  Moon. 

The  length  of  one  mile  on  the  Moon  would,  as  seen  from  the  Earth, 
subtend  an  angle  of  about  1"  of  arc.  In  order  that  an  object  may  be 
plainly  visible  to  the  naked  eye,  it  must  subtend  an  angle  of  nearly 
60."  Consequently  a  magnifying  power  of  60  is  required  to  render  a 
round  object  one  mile  in  diameter  on  the  surface  of  the  Moon  plainly 
visible. 

The  following  table   shows  the  diameters  of  the  smallest  objects 


I.  FIRST  QUADRANT. 

1.  Pallas 

2.  Gambart 

3.  Stadius 

4.  Copernicus 

5.  Reinhold 

6.  Kepler 

7.  Hevelius 

8.  Eratosthenes 

9.  Marius 

10.  Archimedes 

11.  Timocharis 

12.  Euler 

13.  Aristarchus 

14.  Herodotus 

15.  Laplace 

16.  Hei-aclides 

17.  Bianchini 

18.  Sharp 
l.».  Mairan 

20.  Plato 

21.  Condamine 

22.  Harpalus 


LIST   OF   LUNAR   CRATERS,  E 

N.  B.— The  Quadrants  are  marked  I,  II,  III,  IV  on  the  borders  of  the  Map. 


N.  B.— From  new  moon  (Odays) 
to  full  moon  (15")  the  west  limb  of 
the  moon  is  fully  lighted.  The 
position  of  the  terminator  for 
each  intermediate  day  Is  marked 
by  the  upper  set  of  numbers 
along  the  moon's  equator  :  2,  3, 
4  .  .  15  From  full  moon  to  the 
following  new  moon  the  east 


SOUT 


II.  SECOND  QUADRANT. 

51.  Moretus 

52.  Cysatus 

53.  Blancanus 

54.  Scheirier 

55.  Clavius 

56.  Maginus 

57.  Longomontanus 

58.  Schiller 

59.  Phocylides 

60.  Wargentin 

61.  Saussure 

62.  Pictet 

63.  Tycho 
61.  Heinsius 

65.  Hainzel 

66.  Schickard 

67.  Hell 

68.  Gauricus 

69.  Wurzelbauer 

70.  Pitatus 

71.  Hesiodus 

72.  Clchus 

73.  Capuanus 

74.  Ramsden 

75.  Vitello 

76.  Regiomontanus 

77.  Purbach 

78.  Thebit 

79.  Mercator 

80.  Campanus 

81.  Bullialdus 

82.  Doppelmayer 

83.  Fourier 

84.  Vieta 

85.  Mersenius 

86.  Arzachel 

87.  Alphonsus 

88.  Alpetragius 

89.  Davy 

90.  Guericke 

91.  Lubiniezky 

92.  Gassendi 

93.  Billy 

94.  Hansteen 

95.  Sirsalis 

96.  Ptolemseus 

97.  Herschel 

98.  Moesting 

99.  Lalande 
100.  Damoiseau 


*  The  names  are  those 
of  scientific  men,  usually 
of  astronomers. 


NOR 

FIG.  178.  —THE  MOON  AS 


SHOWN   IN   FIG.    178.* 

see  the  numbers  plainly,  a  common  hand-glass  should  be  used. 


III.  THIRD  QUADRANT. 
101.  Manzinus 


limb  is  fully  lighted,  and    the 
position  of  the  terminator  for     m%   jiutus 
each  intermediate  day  is  marked     103>  Boussingault 
by  the   lower  set  of  numbers ;     jo4   Boguslawsky 
17,  18  ...  28,  30.    These  numbers     iQ5.  Curtius 
give  the   moon's  age,  in  days,     jog   Zach 
when    the     terminator     passes     107.  Jacob! 
through  their  positions  on  the     jog   Lilius 
map.  109.  Baco 

v  110.  Pitiscus 

111.  Hommel 
IV-Y\  112.  Fabricius 

n  113.  Metius 

N%A    \  114.  Rheita 

\  115.  Nicolai 

\  116.  Barocius 

' C" >;  -\  117.  Maurolycus 

\  118.  Clairaut 

,  \  119.  Cuvier 

120.  Stoeffler 

121.  Funerius 
a'  A         '                                           122.  Riccius 

\  123.  Zagut 

\  124.  Lindenau 

\  125.  Aliacenus 

^     \  126.  Werner 

•£  127.  Apianus 

"V    *•      ,  128.  Sacrobosco 

129.  Santbach 

^     \  130.  Fracastor 

!fc>-;  ••'-••;•  131.  Petavius 

;  132.  Vendelinus 

\  133.  Langrenus 

•M.  134.  Goclenius 

\  135.  Guttenberg 

w   .  \  136.  Theophilus 

1S7.  Cyrillus 

138.  Catherina 

139.  Albategnius 

140.  Parrot 

141.  Hipparchus 

142.  Reaumur 

143.  Delambre 


IV.  FOURTH  QUADRANT. 

151.  Taruntius 

152.  Sabine 

153.  Ritter 

154.  Arago 

155.  Ariadeeufc 

156.  Godin 

157.  Agrippa 

158.  Hyginus 

159.  Triesnecker 

160.  Condorcet 

161.  Azout 

162.  Picard 

163.  Vitruvius 

164.  Plinius 

165.  Acherusia 

166.  Menelaus 

167.  Manilius 

168.  Einmart 

169.  Cleomedes 

170.  Macrobius 

171.  Roemer 

172.  Le  Monnier 

173.  Linnaeus 

74.  Bessel 

75.  Gauss 

76.  Messala 

77.  Geminus 

78.  Posidonius 

179.  Calippus 

180.  Aristillus 

181.  Autolycus 

182.  Cassini 

183.  Atlas 

184.  Hercules 

185.  Franklin 

186.  Burg 

187.  Eudoxus 

188.  Aristotle 

189.  Endymion 


THE  MOON.  319 

that  can  be  seen  with  different  magnifying  powers,  at  the  Moon's 
distance. 

Power      60  ;  diameter  of  object  1  mile. 

Power    150  ;  diameter  2000  feet. 

Power    500  ;  diameter  600  feet. 

Power  1000  ;  diameter  300  feet. 

If  telescopic  power  could  be  increased  indefinitely,  there  would  be 
no  limit  to  the  minuteness  of  an  object  that  could  be  seen  on  the 
Moon's  surface.  But  the  imperfections  of  all  telescopes  are  such  that 
only  in  exceptional  cases  can  anything  be  gained  by  increasing  the  mag- 
nifying power  beyond  1000.  The  influence  of  warm  and  cold  currents 
in  our  atmosphere  will  forever  prevent  the  advantageous  use  of  very 
high  magnifying  powers. 

Character  of  the  Moon's  Surface. — The  most  striking  point  of  dif- 
ference between  the  Earth  and  Moon  is  seen  in  the  total  absence 
from  the  latter  of  anything  that  looks  like  the  water-worn  surfaces 
of  terrestrial  plains,  prairies,  and  hills.  Valleys  and  mountain- 
chains  exist  on  the  Moon,  but  they  are  abrupt  and  rugged,  not  in  the 
least  like  our  formations  of  the  same  name.  The  lowest  surface  of 
the  Moon  which  can  be  seen  with  the  telescope  appears  to  be  nearly 
smooth  and  flat,  or,  to  speak  more  exactly,  spherical  (because  the 
Moon  is  a  sphere).  This  surface  has  different  shades  of  color  in 
different  regions.  Some  portions  are  of  a  bright  silvery  tint,  while 
others  have  a  dark  gray  appearance.  These  differences  of  tint  seem 
to  arise  chiefly  from  differences  of  material. 

Upon  this  surface  as  a  foundation  are  built  numerous  formations 
of  various  sizes,  usually  of  a  very  simple  character.  Their  general 
form  can  be  made  out  by  the  aid  of  Fig.  179,  and  their  dimensions  by 
remembering  that  one. inch  on  the  figure  is  about  30  miles.  The 
largest  and  most  prominent  features  are  known  as  craters.  They 
have  a  typical  form  consisting  of  a  round  or  oval  rugged  wall  rising 
from  the  plain  in  the  manner  of  a  circular  fortification.  These 
walls  are  frequently  10,000  feet  or  more  in  height,  very  rough  and 
broken.  In  their  interior  we  see  the  plane  surface  of  the  Moon 
already  described.  It  is,  however,  generally  strewn  with  fragments 
or  broken  up  by  chasms. 

In  the  centre  of  the  craters  we  frequently  find  a  conical  formation 
rising  up  to  a  considerable  height.  The  craters  resemble  the  vol- 
canic formations  upon  the  Earth,  the  principal  difference  being  that 
some  of  them  are  very  much  larger  than  anything  known  here. 
The  diameter  of  the  larger  ones  ranges  from  50  to  100  miles,  while 
the  smallest  are  a  half-mile  or  less,  in  diameter— mere  crater-pits. 


320  ASTRONOMY. 

Heights  of  the  Lunar  Mountains.— When  the  Moon  is  only  a  few 
days  old,  the  Sun's  rays  strike  very  obliquely  upon  the  lunar  moun- 
tains, and  they  cast  long  shadows.  From  the  known  position  of 
the  Sun,  Moon,  and  Earth,  and  from  the  measured  length  of  the 
shadows,  the  heights  of  the  mountains  can  be  calculated.  It  is  thus 
found  that  some  of  the  mountains  near  the  south  pole  rise  to  a 
height  of  8000  or  9000  metres  (from  25,000  or  30,000  feet)  above  the 
general  surface  of  the  Moon.  Heights  of  from  3000  to  7000  metres 
are  very  common  over  almost  the  whole  lunar  surface. 

Is  there  any  Change  on  the  Surface  of  the  Moon  ? — When  the  sur- 
face of  the  Moon  was  first  found  to  be  covered  by  craters  like  the 
volcanoes  of  the  Earth,  it  was  very  naturally  thought  that  the  lunar 
volcanoes  might  be  still  in  activity,  and  exhibit  themselves  to  our 
telescopes  by  their  flames.  Not  the  slightest  evidence  of  any  erup- 
tion at  the  Moon's  surface  has  been  found. 

Several  instances  of  supposed  changes  of  shape  of  features  on  the 
Moon's  surface  have  been  described  in  recent  times,  however. 

Photographs  of  the  Moon. — To  make  a  complete  map  of  the  Moon 
requires  a  lifetime.  The  map  of  the  Moon  (six  feet  in  diameter) 
made  by  Dr.  SCHMIDT,  Director  of  the  Observatory  of  Athens,  occu- 
pied the  greater  part  of  his  time  during  the  years  1845-1865. 

A  photograph  of  the  full  moon  can  now  be  taken  in  a  fraction  of  a 
second  that  shows  most  features  far  better  than  SCHMIDT'S  map; 
and  a  series  of  such  photographs  exhibits  substantially  every  lunar 
feature  better  than  any  map  can  do.  The  first  photographs  of  the 
Moon  were  made  in  America.  The  best  lunar  photographs  are 
those  of  the  observatories  of  Mt  Hamilton  (Lick  Observatory)  and 
of  Paris. 

Key-chart  of  the  Moon.— The  accompanying  chart  of  the  Moon  will 
be  found  of  use  to  the  student  who  has  a  small  telescope  or  even  an 
opera-glass  at  his  command.  After  acquiring  a  general  acquaintance 
with  the  lunar  topography  by  observations  continued  throughout  a 
lunation,  he  should  begin  to  study  the  craters  in  detail,  making 
drawings  of  them  as  accurately  as  he  can.  Such  drawings  may  not 
be  of  value  to  science,  but  they  will  be  invaluable  to  the  student 
himself;  for  they  will  train  him  to  see  what  is  to  be  seen,  and  to 
register  it  accurately.  The  changes  in  the  appearance  of  lunar 
craters  during  a  lunation  are  very  marked,  and  to  seek  the  explana- 
tion of  each  particular  change  is  a  valuable  discipline. 

GALILEO  supposed  some  of  the  plains  of  the  Moon  to  be  seas,  and 
named  them  Mare  Tranquilitatis  (the  tranquil  sea),  etc.  The  prin- 
cipal mountain-chains  on  the  Moon  are  named  Apennines,  Alps,  Cau- 


THE  MOON, 


321 


FIG.  179.— A  DRAWING  OF  THE  LUNAR  SURFACE. 


322 


ASTRONOMY. 


casus,  etc.     The  craters  are  usually  named  after  noted  astronomers, 
Kepler,  Copernicus,  Tycho. 

34.  The  Minor  Planets. — We  have  next  to  consider  the 
group  of  minor  planets,  also  called  asteroids  (because  they 
resemble  stars  in  appearance)  or  planetoids  (because  they 
are  planets).  None  of  them  was  known  nntil  the  begin- 
ning of  the  nineteenth  century. 

First  of  all,  a  curious  relation  between  the  distances  of  the  planets, 
known  as  BODE'S  law,  must  be  mentioned.  If  to  the  numbers 

0,  3,  6,  12,  24,  48,  96,  192,  384, 

each  of  which  (the  second  excepted)  is  twice  the  preceding,  we  add 
4,  we  obtain  the  series 

4.  7,  10,  16,  28,  52,  100,  196,  388, 

These  last  numbers  represent  approximately  the  distances  of  the 
planets  from  the  Sun  (except  for  Neptune,  which  was  not  discovered 
when  the  law  was  announced)  by  BODE  in  1772. 

This  is  shown  in  the  following  table  : 


PLANETS. 

Actual 
Distance. 

BODE'S  Law. 

3  9 

A    ft 

7.2 

7  0 

Earth                  

10  0 

10  0 

Mars  .. 

15  2 

16  0 

27  7 

28  0 

52  0 

52  0 

95  4 

100  0 

191  8 

196  0 

300  4 

388  0 

Although  the  so-called  law  was  purely  arbitrary,  the  agreement 
between  the  distances  predicted  by  the  law  and  the  actual  distances 
was  sufficiently  close  to  draw  attention  to  tlie  fact  that  a  jrap  existed 
in  the  succession  of  the  planets  between  Mars  and  Jupiter. 

It  was  therefore  supposed  by  the  astronomers  of  the 
seventeenth  and  eighteenth  centuries  that  a  new  major 
planet  might  be  found  in  the  region  between  Mars  and 


THE  MINOR  PLANETS.  323 

Jupiter.  A  search  for  this  object  was  instituted,  but  before 
it  had  made  much  progress  a  minor  planet  in  the  place  of 
the  one  so  long  expected  was  found  by  PIAZZI,  of  Palermo. 
The  discovery  was  made  on  the  first  day  of  the  present 
century,  1801,  January  1.  It  was  named  Ceres. 

In  the  course  of  the  following  seven  years  the  astronom- 
ical world  was  surprised  by  the  discovery  of  three  other 
planets,  all  in  the  same  region,  though  not  revolving  in  the 
same  orbit.  Seeing  four  small  planets  where  one  large  one 
ought  to  be,  OLBERS  suggested  that  these  bodies  might  be 
fragments  of  a  large  planet  that  had  been  broken  to  pieces 
by  the  action  of  some  unknown  force. 

A  generation  of  astronomers  now  passed  away  without 
the  discovery  of  more  than  these  four.  It  was  not  until 
1845  that  a  fifth  planet  of  the  group  was  found.  In  1847 
three  more  were  discovered,  and  many  discoveries  have 
since  been  made.  The  number  is  now  nearly  500,  and 
the  discovery  of  additional  ones  is  going  on  as  fast  as  ever. 
The  frequent  announcements  of  the  discovery  of  planets 
which  appear  in  the  public  prints  all  refer  to  bodies  of  this 
group.  Seventy-seven  of  them  have  been  discovered  by 
American  astronomers. 

The  minor  planets  are  distinguished  from  the  major  ones 
by  many  characteristics.  Among  these  we  may  mention 
their  small  size;  their  positions,  all  but  one  being  situated 
between  the  orbits  of  Mars  and  Jupiter;  the  great  eccen- 
tricities and  inclinations  of  their  orbits.  The  inclination 
of  the  orbit  of  Pallas  to  the  ecliptic  is  35°,  for  example. 

Number  of  Small  Planets.— It  would  be  interesting  to  know  how 
many  of  these  planets  there  are  in  the  group,  but  it  is  as  ret  impos- 
sible even  to  guess  at  the  number.  As  already  stated,  about  500  are 
now  known,  and  new  ones  are  found  every  year. 

A  minor  planet  presents  no  sensible  disk,  and  therefore  looks 
exactly  like  a  small  star.  It  can  be  detected  only  by  its  motion  among 
the  surrounding  stars,  which  is  so  slow  that  some  hours  must  elapse 
before  it  can  be  noticed.  Nowadays  they  are  found  by  photograph- 


324:  ASTRONOMY. 

ing  a  region  of  the  sky  with  two  or  three  hours'  exposure  and  noticing 
whether  any  of  the  objects  on  the  plate  show  a  motion  in  that  time. 
A  fixed  star  will  show  no  motion.  An  asteroid  will  make  a  trail  on 
the  plate. 

Magnitudes.— It  is  impossible  to  make  any  precise  measurement  of 
the  diameters  of  the  minor  planets.  The  diameters  in  miles  that  are 
sometimes  quoted  are  subject  to  very  large  errors.  The  amount 
of  light  which  the  planet  reflects  is  a  better  guide  than  measures 
made  with  ordinary  micrometers.  Supposing  the  proportion  ol  light 
reflected  to  be  the  same  as  in  the  case  of  the  larger  planets,  the  diam- 
eters of  the  three  or  four  largest  range  between  300  and  600  kilo- 
metres, while  the  smallest  are  from  20  to  50  kilometres  in  diameter. 
The  average  diameter  is  perhaps  less  than  150  kilometres  (say  90 
miles)  ;  that  is,  scarcely  more  than  one  hundredth  that  of  the  Earth. 
The  volumes  of  solid  bodies  vary  as  the  cubes  of  their  diameters  ;  it 
might  therefore  take  a  million  of  these  planets  to  make  one  of  the 
size  of  the  Earth. 

Mass  and  Density  of  the  Asteroids. — Nothing  is  known  of  the  mass 
of  any  single  asteroid.  If  their  density  is  the  same  as  that  of  the 
Earth  the  mass  of  the  larger  asteroids  will  be  about  ¥^o  °f  tlie 
Earth's  mass.  The  force  of  gravity  on  the  surface  of  such  a  body 
would  be  about  -fa  of  the  force  of  gravity  on  the  Earth.  A  bullet 
shot  from  a  rifle  would  fly  quite  away  from  the  planet  and  would  cir- 
culate about  the  Sun.  It  is  not  probable  that  any  of  them  has 
an  extensive  atmosphere. 


CHAPTER   XIX. 

THE   PLANETS  JUPITER,    SATURN,    URANUS,    AND 
NEPTUNE. 

35.  Jupiter. — Jupiter  is  much  the  largest  planet  in  the 
system.  His  mean  distance  is  483,300,000  miles.  His 
mean  diameter  is  86,500  miles,  the  polar  diameter  being 
83,000,  the  equatorial  88,200  miles.  His  linear  diameter 
is  about  y1^,  his  surface  is  y^-,  and  his  volume  y^o  tna^  of 
the  Sun.  His  mass  is  ToVs-  His  density  is  nearly  the 
same  as  the  Sun's  density,  that  is  1T3^  times  the  density 
of  water.  The  densities  of  Venus,  the  Earth,  the  Moon, 
and  of  Mars  are  all  more  than  three  times  the  density  of 
water.  A  cubic  foot  of  the  materials  of  each  of  these 
bodies  weighs  at  least  200  Ibs.  A  cubic  foot  of  the  stuff 
out  of  which  Jupiter  is  made  weighs,  on  the  average,  no 
more  than  83  Ibs.  Jupiter  is,  in  this  respect,  like  the  Sun 
and  not  like  the  inner  planets. 

He  is  attended  by  five  satellites,  four  of  which  were  dis- 
covered by  GALILEO  on  January  7,  1610.  He  named  them, 
in  honor  of  the  MEDICIS,  the  Medicean  stars.  They  are 
now  known  as  Satellites  I,  II,  III,  and  IV,  I  being  the 
nearest.  They  are  large  bodies,  from  2100  to  3500  miles 
in  diameter,  comparable  in  size  to  the  Moon  or  to  Mercury. 
The  fifth  satellite  was  discovered  by  BARNAHD  with  the 
great  telescope  of  the  Lick  Observatory  in  1892.  It  is  a 
very  small  object,  about  100  miles  in  diameter,  revolving 
very  close  to  the  surface  of  Jupiter.  Observations  show 
that  the  larger  satellites  revolve  about  Jupiter ',  always  turn- 

325 


326  ASTRONOMY. 

ing  the  same  face  to  the  planet  just  as  our  own  Moon  tarns 
always  the  same  face  to  the  Earth. 

The  rotation-time  of  the  planet  is  not  the  same  in  all  latitudes  ; 
nor,  in  the  same  latitude,  at  all  depths  below  the  outer  surface  of  its 
clouds.  The  average  time  of  rotation  is  about  9h  55m,  which  is  notice- 
ably shorter  than  the  rotation-times  of  Mars  and  the  Earth.  The 


PIG.  180.— DRAWING  OF  JUPITER  MADE  AT  THE  LICK  OBSERVA- 
TORY, AUGUST  28,  1890. 

figure  of  the  planet  is  markedly  spheroidal  ;  its  disk  is  easily  seen  to 
be  elliptical  in  shape.  The  pJiases  of  Jupiter  are  slight — scarcely 
noticeable.  The  reflecting- power  (albedo}  of  the  planet  is  -ffa,  not 
very  much  less  than  that  of  newly  fallen  snow  (TW).  In  this  respect 
Jupiter  and  all  the  outer  planets  differ  very  materially  from  Mars 
and  all  the  inner  planets  (except  Venus).  The  periodic-time  of  Jupiter 


Tfffi  PLANET  JUPITER.  327 

is  11.86  years,  about  the  period  in  which  the  solar  spots  vary  from 
maximum  to  maximum  again.  Figure  180  shows  in  the  upper  third 
of  the  disk  an  oval  spot  that  has  remained  on  the  planet  for  the  past 
30  years  (The  Great  Red  Spot).  Its  surface  is  red  and  it  probably  lies 
at  a  deeper  level  than  many  of  the  whitish  clouds  in  the  same  lati- 
tudes. It  is  remarkable  that  the  red  spot  has  endured  for  so  long  a 
time  on  the  surface  of  the  planet  where  all  other  features  are  so 
changeable.  The  red  spot  is  not  fixed  in  position,  but  is  slowly  drift- 
ing to  the  east.  It  is  as  if  Australia  were  slowly  moving  eastwardly 
on  the  earth.  The  rotation  time  of  the  red  spot  was  9h  55m  34».5  in 
1869  ;  34s. 1  in  1879  :  39s.O  in  1884  ;  40-.4  in  1889  ;  4KO  in  1894  ;  41'.9 
in  1898.  It  is  as  if  an  island  of  slag  were  drifting  on  the  surface  of 
a  lake  of  liquid  lava. 

The  temperature  of  Jupiter  is,  in  all  probability,  very 
high.  The  planet  may  even  be  incandescent.  The  rapid 
changes  observed  in  the  surface  of  Jupiter  prove  that  the 
visible  surface  is  gaseous — an  atmospheric  envelope.  These 
changes  are  due  to  heat.  As  the  solar  heat  at  Jupiter  is 
only  -jif  of  the  solar  heat  at  the  Earth,  it  is  likely  that  the 
changes  are  due  to  the  internal  heat  of  the  planet  itself. 
The  solar  heat  at  Saturn  is  only  -fa  of  the  solar  heat  at  the 
Earth,  and  as  it  is  also  surrounded  by  a  gaseous  envelope, 
there  is  good  reason  for  supposing  Saturn,  also,  to  be  a  hot 
body. 

The  surface  of  Jupiter  has  been  carefully  studied  with 
the  telescope,  particularly  within  the  past  thirty  years. 
Although  further  from  us  than  Mars,  many  of  the  details 
on  his  disk  are  much  more  plainly  marked.  The  most 
characteristic  features  are  shown  in  the  drawings  appended. 
These  features  are,/r,tf,  the  dark  bands  of  his  equatorial 
regions,  and,  secondly,  the  cloud-like  forms  spread  over 
nearly  the  whole  surface.  Near  the  edges  of  the  disk  all 
these  details  become  indistinct,  and  finally  vanish,  thus  in- 
dicating a  highly  absorptive  atmosphere  lik^  that  of  the  Sun. 
The  light  from  the  centre  of  the  disk  is  twice  as  bright  as 
that  from  the  poles.  The  bands  can  be  seen  with  instru- 


328  ASTRONOMY. 

ments  no  more  powerful  than  those  used  by  GALILEO,  yet 
he  makes  no  mention  of  them. 

The  general  color  of  the  bands  is  reddish.  Their  posi- 
tion varies  slightly  in  latitude,  but  in  the  main  they  remain 
as  permanent  features  of  the  region  to  which  they  belong. 


FIG.  181  — VIEW  OP  JUPITER  AND  HIS  SATELLITES  IN  A  SMALL 
TELESCOPE. 

HERSCHEL,  in  the  year  1793,  attributed  the  aspects  of 
the  bands  to  zones  of  the  planet's  atmosphere  more  tranquil 
and  less  filled  with  clouds  than  the  remaining  portions,  so 
as  to  permit  the  true  surface  of  the  planet  to  be  seen 
through  these  zones,  while  the  clouds  prevailing  in  the 
other  regions  give  a  brighter  tint  to  the  latter.  It  is  not 
likely  that  we  see  the  true  surface  of  the  planet,  in  the 
belts,  but  rather  the  outer  surfaces  of  the  inner  layers  of 
the  planet's  atmosphere. 

The  clouds  themselves  can  easily  be  seen  at  times,  and 
they  have  every  variety  of  shape.  In  general  they  are 
similar  in  form  to  a  series  of  white  cumulus  clouds  such  as 
are  frequently  seen  piled  up  near  the  horizon,  and  the 
spaces  between  them  have  the  deep  salmon  color  of  the 
spaces  between  cumulus  clouds  before  a  summer  storm. 
This  color  is  due  to  the  absorption  of  the  dense  atmosphere 
of  the  planet,  probably.  The  bands  themselves  and  the  red 


THE  PLANET  JUPITER.  329 

spot  seem  frequently  to  be  veiled  over  with  something  like 
the  thin  cirrus  clouds  of  our  atmosphere. 

Such  clouds  can  be  tolerably  accurately  observed,  and 
may  be  used  to  determine  the  rotation-time  of  the  planet. 
The  observations  show  that  the  clouds  often  have  a  proper 
motion  of  their  own. 


FIG.  182. — VIEW  OP  JUPITER  IN  A  LARGE   TELESCOPE,  WITH  A 
SATELLITE  AND  ITS  SHADOW  SEEN  ON  THE  DISK. 

Motions  of  the  Satellites. — The  satellites  move  about  Jupiter  from 
west  to  east  in  nearly  circular  orbits.  When  one  of  these  satellites 
passes  between  the  Sun  and  Jupiter,  it  casts  a  shadow  upon  Jupiter's 
disk  (see  Fig.  182)  precisely  as  the  shadow  of  our  Moon  is  thrown  upon 
the  Earth  in  a  solar  eclipse.  If  the  satellite  passes  through  Jupiter's 
own  shadow  in  its  revolution,  an  eclipse  of  the  satellite  takes  place. 
If  it  passes  between  the  Earth  and  Jupiter,  it  is  projected  upon  Ju- 
piter's disk,  and  we  have  a  transit  of  the  satellite  (see  Fig,  182);  itJu- 


330 


ASTRONOMY. 


piter  is  between  the  Earth  and  the  satellite,  an  occultation  of  the 
latter  occurs.  All  these  phenomena  can  be  seen  with  a  common 
telescope,  and  the  times  are  predicted  in  the  Nautical  Almanac. 
These  shadows  are  seen  black  upon  Jupiter's  surface  by  contrast, 
because  Jupiter  is  very  much  brighter  than  the  satellites. 


Fia  183  —THE  ECLIPSES  OF  JUPTTETC'S  SATELLITES. 

S  is  the  Sun,  T  the  Earth,  J,  J'.  J",  J'"  are  different  positions  of  Jupiter. 


Telescopic  Appearance  of  the  Satellites.— Under  ordinary  circum- 
stances, the  satellites  of  Jupiter  are  seen  to  have  disks  ;  under  very 
favorable  conditions,  markings  have  been  seen  on  these  disks. 

The  satellites  completely  disappear  from  telescopic  view  when  they 
enter  the  shadow  of  the  planet.  This  shows  that  neither  planet  nor 
satellite  is  self-luminous  to  any  marked  degree.  If  the  satellite  were 


THE  PLANET  SATURN.  331 

self-luminous,  it  would  be  seen  by  its  own  light ;  and  if  the  planet 
were  luminous,  the  satellite  might  be  seen  by  the  reflected  light  of 
the  planet. 

The  Progressive  Motion  of  Light.— The  discovery  that  light  requires 
time  to  travel  was  first  made  by  the  observations  of  the  satellites  of 
Jupiter,  as  has  been  said.  (See  page  255.)  Jupiter  casts  a  shadow 
just  as  our  Earth  does,  and  its  inner  satellite  passes  through  this 
shadow  and  is  eclipsed  at  every  revolution. 

The  eclipses  can  be  observed  from  the  Earth,  the  satellite  vanishing 
from  view  as  it  enters  the  shadow,  and  reappearing  when  it  leaves  it. 
The  astronomers  of  the  seventeenth  century  made  tables  by  which 
the  times  of  the  eclipses  could  be  predicted.  It  was  found  by  ROMER 
that  these  times  depended  on  the  distance  of  Jupiter  from  the  Earth. 

When  the  Earth  was  nearest  Jupiter,  the  eclipses  were  seen  earlier 
than  the  predicted  time.  Jupiter  and  the  Earth  were  near  each  other. 
When  the  Earth  was  farthest  from  Jupiter  the  eclipses  were  seen 
later  than  the  predicted  time.  Jupiter  and  the  Earth  were  far  apart. 

The  light  from  the  satellite  required  time  to  cross  the  intervening 
spaces.  The  velocity  with  which  light  travels  is  186,330  miles  per 
second.  At  that  rate  it  traverses  the  distance  from  the  Sun  to  the 
Earth  in  499  seconds.  The  sunlight  is  8m  198  old  when  it  reaches  us. 

Longitudes  by  Observation  of  the  Satellites  of  Jupiter. — Tbe  differ- 
ence of  longitude  of  two  places  on  the  Earth  is  the  difference  of  their 
simultaneous  local  times.  If  we  know  beforehand  (by  calculation)  the 
Greenwich  time  of  an  eclipse  of  one  of  the  satellites — and  if  we  observe 
the  eclipse  by  a  clock  keeping  our  own  local  time,  the  difference  of 
the  two  times  (observed  and  calculated)  is  our  longitude  from  Green- 
wich. GALILEO  suggested  that  a  method  like  this  might  be  useful 
in  determining  terrestrial  longitudes  and  the  method  has  often  been 
tested.  The  difficulty  of  observing  the  eclipses  with  accuracy,  and 
the  fact  that  the  aperture  of  the  telescope  employed  has  an  important 
effect  on  the  appearances  seen,  have  so  far  kept  this  method  from  a 
wide  utility,  which  it  at  first  seemed  to  promise. 

36.  Saturn  and  its  System, — Saturn  is  the  most  distant 
of  the  major  planets  known  to  the  ancients.  It  revolves 
around  the  Sun  in  29£  years,  at  a  mean  distance  of  about 
886,000,000  miles.  The  equatorial  diameter  of  the  ball  of 
the  planet  is  about  75,000  miles  and  the  polar  diameter 
about  68,000  miles.  It  revolves  on  its  axis  in  10h  14m  24% 
or  less  than  half  a  day,  which  accounts,  as  in  the  case  of 


332 


ASTRONOMY. 


FIG.  184.— DRAWING  OF  SATURN  MADE  AT  THE  LICK  OBSERVA- 
TORY, JANUARY  7,  1888, 


THE  PLANET  SATURN.  333 

Jupiter,  for  the  ellipticity  of  the  disk.  The  mass  of  the 
planet  is  only  95  times  the  mass  of  the  Earth,  though  its 
volume  is  760  times  greater.  The  force  of  gravity  at  its 
surface  is  only  a  little  greater  than  that  of  the  Earth.  It 
is  remarkable  for  its  small  density,  which  is  less  than  that 
of  any  other  heavenly  body,  and  even  less  than  that  of 
water.  No  doubt  the  planet  is  in  great  part,  if  not  en- 
tirely, gaseous.  The  edges  of  the  planet  are  fainter  than 
the  centre,  as  in  the  case  of  Jupiter,  and  for  the  same 
reason. 


FIG.  185. — VIEW  OF  THE  SATURNIAN  SYSTEM  IN  A  SMALL  TELE- 
SCOPE. 


Saturn  is  the  centre  of  a  system  of  its  own,  in  appearance 
quite  unlike  anything  else  in  the  heavens.  Its  most  note- 
worthy feature  is  a  pair  of  rings  which  surround  it  at  a 
considerable  distance  from  the  planet  itself.  Outside  of 
these  rings  revolve  no  less  than  nine  satellites.  The 


334  ASTRONONT. 

planet,  rings,  and  satellites  are  altogether  called  the 
Saturnian  system.  The  general  appearance  of  this  system, 
as  seen  in  a  small  telescope,  is  shown  in  Fig.  185.  Fig. 
184  was  drawn  with  the  great  telescope  of  the  Lick 
Observatory. 

The  Kings  of  Saturn. — The  rings  are  the  most  remark- 
able and  characteristic  feature  of  the  Saturnian  system. 
Fig.  186  gives  two  views  of  the  ball  and  rings.  The  upper 
one  shows  one  of  their  aspects  as  actually  presented  in  the 
telescope,  and  the  lower  one  shows  what  the  appearance 
would  be  if  the  planet  were  viewed  from  a  direction  at  right 
angles  to  the  plane  of  the  ring  (which  it  never  can  be  from 
the  Earth).  The  shadow  of  the  ball  of  the  planet  on  the 
rings  should  be  noticed  in  both  views.  The  periodic-time 
of  the  planet  is  a  little  less  than  29|  years. 

The  first  telescopic  observers  of  Saturn  were  unable  to  see  the 
rings  in  their  true  form,  and  were  greatly  perplexed  to  account  for 
the  appearance  which  the  planet  presented.  GALILEO  described  the 
planet  as  "  tri-corporate,"  the  two  ends  of  the  ring  having,  in  his 
imperfect  telescope,  the  appearance  of  a  pair  of  small  planets  attached 
to  the  central  one.  "  On  each  side  of  old  Saturn  were  servitors  who 
aided  him  on  his  way."  This  discovery  was  announced  to  his  friend 
KEPLER  in  this  logogriph  : 

"smaismrmilmepoetalevmibunenugttaviras,"  which,  being  trans- 
posed, becomes — 

"  Altissimum  planetam  tergeminum  observavi  "  (I  have  observed 
the  most  distant  planet  to  be  tri-form). 

The  phenomenon  constantly  remained  a  mystery  to  its  first  ob- 
server. In  1610  he  had  seen  the  planet  accompanied,  as  he  supposed, 
by  two  lateral  stars  ;  in  1612  the  latter  had  vanished  and  the  central 
body  alone  remained.  GALILEO  inquired  "whether  Saturn  had 
devoured  his  children,  according  to  the  legend." 

It  was  not  until  1655  (after  seven  years  of  observation)  that  the 
celebrated  HUYGHENS  discovered  the  true  explanation  of  the  remark- 
able and  recurring  series  of  phenomena  present  by  the  tri  corporate 
planet. 


THE  PLANET  SATURN. 


335 


FIG.  186.— THE  PLANET  SATURN. 

1°  as  it  sometimes  appears  to  an  observer  on  the  Earth ;  2°  as  it  would 
appear  to  an  observer  over  the  polar  region  of  the  planet. 


336  ASTRONOMY. 

He  announced  his  conclusions  in  the  following  logogriph  : 

"  aaaaaa  ccccc  d  eeeee  g  h  iiiiiii  1111  mm  nnnnnnnnn  oooo  pp  q  rr  s 
ttttt  uuuuu,"  which,  when  arranged,  read — 

"  Annulo  cingitur,  tenui,  piano,  nusquam  coherente,  ad  eclipticam 
inclinato"  (it  is  girdled  by  a  thin  plane  ring,  nowhere  touching, 
inclined  to  the  ecliptic). 

This  description  is  complete  and  accurate,  as  to  the  appearance  in  a 
small  telescope. 

In  1675  it  was  found  by  CASSINI  that  what  HUYOHENS  had  seen  as 
a  single  ring  was  really  two.  A  division  extended  all  the  way  around 
near  the  outer  edge.  The  division  is  shown  in  the  figures.  This 
division  is  permanent.  Others  are  sometimes  seen  at  different  places 
and  this  fact  of  observation  suggests  that  the  rings  cannot  be  per- 
manent solids,  nor  liquids. 

In  1850  the  Messrs.  BOND,  of  Harvard  College  Observatory,  found 
that  there  was  a  third  ring,  of  a  dusky  and  nebulous  aspect,  attached 
to  the  inner  edge  of  the  inner  ring.  It  is  known  as  Bond's  dusky  ring. 
It  is  a  difficult  object  to  see  in  a  small  telescope.  It  is  not  separated 
from  the  bright  ring,  but  attached  to  it.  The  latter  shades  off  toward 
its  inner  edge,  and  merges  gradually  into  the  dusky  ring,  Fig.  184. 

Aspect  of  the  Rings. — As  Saturn  revolves  around  the  Sun,  the 
plane  of  the  rings  remains  parallel  to  itself.  That  is,  if  we  consider 
a  straight  line  passing  through  the  centre  of  the  planet,  perpendicu- 
lar to  the  plane  of  the  ring,  as  the  axis  of  the  latter,  this  axis  will 
always  point  in  the  same  direction  in  space — among  the  stars.  In 
this  respect  the  motion  is  similar  to  that  of  the  Earth  around  the  Sun. 
The  ring  of  Saturn  is  inclined  about  27°  to  the  plane  of  its  orbit. 
Consequently,  as  the  planet  revolves  around  the  sun,  there  is  a 
change  in  the  direction  in  which  the  Sun  shines  upon  it  similar 
to  that  which  produces  the  change  of  seasons  upon  the  Earth,  as 
shown  in  Fig.  110. 

The  corresponding  changes  for  Saturn  are  shown  in  Fig.  187.  Dar- 
ing each  revolution  of  Saturn  (29£  years)  the  plane  of  the  ring 
passes  through  the  Sun  twice.  This  occurred  in  the  years  1878  and 
1891,  at  two  opposite  points  of  the  orbit,  as  shown  in  the  figure, 
and  will  occur  in  1907.  At  two  other  points,  midway  between  these, 
the  Sun  shines  upon  the  plane  of  the  ring  at  its  greatest  inclination, 
about  27°.  Since  the  Earth  (shown  in  the  picture)  is  little  more  than 
one-tenth  as  far  from  the  Sun  as  Saturn  is,  an  observer  sees  Saturn 
nearly,  but  not  quite,  as  if  he  were  upon  the  Sun.  Hence  at  certain 
times  the  rings  of  Saturn  are  seen  edgeways  ;  while  at  other  times 
they  are  at  an  inclination  of  27°,  the  aspect  depending  upon  the  posi- 


THE  PLANET  SATURN. 


337 


tion  of  Saturn  in  its  orbit.  The  following  are  the  times  of  some  of  the 
phases  : 

1878  and  1907.— The  edge  of  the  ring  is  turned  toward  the  Sun.  It 
is  seen  only  as  a  thin  line  of  light. 

1885.— The  planet  having  moved  forward  90°,  the  south  side  of 
the  rings  is  seen  at  an  inclination  of  27°. 

1891.— The  planet  having  moved  90°  further,  the  edge  of  the  ring 
is  again  turned  toward  the  Sun. 


FIG.  187. — DIFFERENT  ASPECTS  OF  THE  RING  OF  SATURN  AS  SEEN 
FROM  THE  EARTH  IN  DIFFERENT  YEARS. 


1899. — The  north  side  of  the  ring  is  inclined  loward  the  sun,  and 
is  seen  at  its  greatest  inclination. 

The  rings  are  extremely  thin  in  proportion  to  their  extent.  Conse- 
quently, when  their  edges  are  turned  toward  the  Earth,  they  appear 
as  a  mere  line  of  light,  which  can  be  seen  only  with  powerful 
telesc  pes. 

Constitution  of  the  Rings  of  Saturn. — The  nature  of 
these  objects  has  been  a  subject  both  of  wonder  and  of  in- 
vestigation by  mathematicians  and  astronomers  ever  since 


338  ASTRONOMY. 

they  were  discovered.  They  were  at  first  supposed  to  be 
solid  bodies;  indeed,  from  their  appearance  it  was  difficult 
to  conceive  of  them  as  anything  else.  The  question  then 
arose :  What  keeps  them  from  falling  on  the  planet  ?  It 
was  shown  mathematically  by  LA  PLACE  that  a  homo- 
geneous and  solid  ring  surrounding  the  planet  could  not 
remain  in  a  state  of  equilibrium,  but  must  be  precipitated 
upon  the  central  ball  by  the  smallest  disturbing  force. 

It  is  now  established  both  by  mathematical  processes  and 
by  spectroscopic  observation  that  the  rings  do  not  form  a 
continuous  mass,  but  are  really  a  countless  multitude  of 
small  separate  particles  or  satellites,  each  of  which  revolves 
in  its  own  orbit.  These  satellites  are  individually  far  too 
small  to  be  seen  in  any  telescope,  but  so  numerous  that 
when  viewed  from  the  distance  of  the  Earth  they  appear  as 
a  continuous  mass,  like  particles  of  dust  floating  in  a  sun- 
beam. 

The  thickness  of  the  rings  is  not  above  100  miles.  The  outer  diam- 
eter of  the  outer  ring  (ring  A)  is  173,000  miles.  It  is  11,500  miles 
wide.  The  CASSINI  division  separating  A  from  B  is  2400  miles  wide. 
The  outer  diameter  of  ring  B  is  145,000  miles,  and  it  is  17,500  miles 
wide.  The  outer  diameter  of  ring  C  (the  dusky  ring)  is  100,000.  and 
its  inner  diameter  is  90,000  miles.  Dr.  KEELER  has  proved,  spectro- 
scopically,  that  different  parts  of  the  rings  revolve  about  the  planet 
at  different  rates,  so  that  the  rings  must  necessarily  be  composed 
of  discrete  particles.  The  rotation  time  of  the  ball  of  Saturn  is  10h 
14m  ;  the  periodic-time  of  the  innermost  particle  of  the  dusky  ring  is 
5h  50m.  Inside  of  this  particle  the  space  is  empty. 

Satellites  of  Saturn. — Outside  of  the  rings  of  Saturn  revolve  its  nine 
satellites,  the  order  and  discovery  of  which  are  shown  in  the  table  on 
page  339. 

The  distances  are  given  in  radii  of  the  planet.  The  satellites  Mimas 
and  Hyperion  and  satellite  No.  9  are  visible  only  in  the  most  power- 
ful telescopes.  The  brightest  of  all  is  Titan,  which  can  be  seen  in  a 
telescope  of  ordinary  size.  The  mass  of  Titan  is  ^Vff  of  Saturn's  mass, 
and  it  is  some  3000  miles  in  diameter.  Japetus  is  nearly  as  bright  as 
Titan  when  west  of  the  planet,  and  is  so  faint  as  to  be  visible  only  in 
large  telescopes  when  on  the  other  side.  Like  our  moon,  it  always 


THE  PLANET  URANUS. 


339 


presents  the  same  face  to  the  planet,  and  one  side  of  it  is  dark  and  the 
other  side  light.  When  west  of  the  planet,  the  bright  side  is  turned 
toward  the  Earth  and  the  satellite  is  visible.  On  the  other  side  of  the 
planet,  the  dark  side  is  turned  toward  us,  and  it  is  nearly  invisible. 
Satellites  3,  4,  5,  6,  and  8  can  be  seen  with  telescopes  of  moderate 
power. 


No. 

NAME. 

Distance 
from 
Planet. 

Discoverer. 

Date  of 
Discovery. 

Periodic-time. 

1 

Mimas 

3.3 

Herschel 

1789 

About    Od  23h 

2 

Enceladus 

4.3 

Herschel 

1789 

ld    9h 

3 

Tethys 

5.3 

Cassini 

1684 

Id21h 

4 

Dione 

6.8 

Cassini 

1684 

2"  18» 

5 

Rhea 

9.5 

Cassini 

1672 

4d  13h 

6 

Titan 

20  7 

Huyghens 

1655 

15d  23h 

7 

Hyperion 

26.8 

Bond 

1848 

21d    7h 

8 

Japetus 

64.4 

Cassini 

1671 

79d    8b 

9 

? 

225.4 

Pickering 

1899 

510  days. 

37.  The  Planet  Uranus, —  Uranus  was  discovered  on 
March  13,  1781,  by  Sir  WILLIAM  HERSCHEL  (then  an 
amateur  observer)  with  a  ten-foot  reflector  made  by  him- 
self. He  was  examining  a  portion  of  the  sky  when  one  of 
the  stars  in  the  field  of  view  attracted  his  notice  by  its 
peculiar  appearance.  On  farther  scrutiny,  it  proved  to  be 
a  planet.  We  can  scarcely  comprehend  now  the  enthusiasm 
with  which  this  discovery  was  received.  No  new  body 
(save  comets)  had  been  added  to  the  solar  system  since  the 
discovery  of  the  third  satellite  of  Saturn  in  1684,  and  all 
the  major  planets  of  the  heavens  had  been  known  for 
thousands  of  years. 

Uranus  revolves  about  the  Sun  in  84  years.  Its  apparent 
diameter  as  seen  from  the  Earth  varies  little,  being  about 
3". 9.  Its  true  diameter  is  about  31,000  miles,  and  its 
figure  is  spheroidal. 

In  physical  appearance  it  is  a  small  greenish  disk  without 
markings.  The  centre  of  the  disk  is  slightly  brighter  than 


340  ASTRONOMY. 

the  edges.  At  its  nearest  approach  to  the  Earth,  it  shines 
as  a  star  of  the  sixth  magnitude,  and  is  just  visible  to  an 
acute  eye  when  the  attention  is  directed  to  its  place.  In 
small  telescopes  with  low  powers,  its  appearance  is  not 
markedly  different  from  that  of  stars  of  about  its  own 
brilliancy. 

Sir  WILLIAM  HERSCHEL  discovered  two  satellites  to 
Uranus.  Two  additional  ones  were  discovered  by  LASSELL 
in  1847. 

Days. 

I.  Ariel  (LASSELL) Period  =    2.520383 

II.    Umbriel     "         "      =    4.144181 

III.  Titania  (HERSCHEL) "      =    8.705897 

IV.  Oberon  "  "      =  13.463269 

Ariel  varies  in  brightness  on  different  sides  of  the  planet, 
and  the  same  phenomenon  has  also  been  suspected  for 
Titania.  This  indicates  that  these  satellites  always 
present  the  same  face  to  the  planet. 

The  most  remarkable  feature  of  the  satellites  of  Uranus 
is  that  their  orbits  are  nearly  perpendicular  to  the  ecliptic 
instead  of  having  a  small  inclination  to  that  plane,  like 
those  of  all  the  orbits  of  both  planets  and  satellites  pre- 
viously known. 

The  four  satellites  move  in  the  same  plane.  This  fact 
renders  it  highly  probable  that  the  planet  Uranus  revolves 
on  its  axis  in  the  same  plane  with  the  orbits  of  the  satel- 
lites, and  is  therefore  an  oblate  spheroid  like  the  Earth. 
If  the  planes  of  the  satellites'  orbits  were  not  kept  together 
by  some  cause,  they  would  gradually  deviate  from  each 
other  owing  to  the  attractive  force  of  the  Sun  upon  the 
planet.  The  different  satellites  would  deviate  by  different 
amounts,  and  it  would  be  extremely  improbable  that  all  the 
orbits  would  be  found  in  the  same  plane  at  any  particular 
epoch.  Since  we  now  see  them  in  the  same  plane,  we  con- 


THE  PLANET  NEPTUNE.  341 

elude  that  some  force  keeps  them  there,  and  the  oblateness 
of  the  planet  is  the  efficient  cause  of  such  a  force. 

The  Planet  Neptune. — After  the  planet  Uranus  had  been 
observed  for  some  thirty  years,  tables  of  its  motion  were 
prepared  by  BOUVARD — a  French  astronomer.  He  had  not 
only  all  the  observations  since  the  date  of  its  discovery  in 
1781,  but  also  observations  extending  back  as  far  as  1695, 
when  the  planet  was  observed  and  supposed  to  be  a  fixed 
star.  It  was  expected  that  the  ancient  observations  would 
materially  aid  in  obtaining  exact  accordance  between  the 
theory  and  observation.  But  it  was  found  that,  after 
allowing  for  all  perturbations  produced  by  the  known 
planets,  the  ancient  and  modern  observations,  though  un- 
doubtedly referring  to  the  same  object,  were  yet  not  to  be 
reconciled  with  each  other,  but  differed  systematically. 
BOUVARD  was  forced  to  found  his  theory  upon  the  modern 
observations  alone.  By  so  doing,  he  obtained  a  good  agree- 
ment between  theory  and  the  observations  of  the  few  years 
immediately  succeeding  1820. 

BOUVARD  made  the  suggestion  that  a  possible  cause  for 
the  discrepancies  noted  might  be  the  existence  of  an 
unknown  planet,  exterior  to  Uranus. 

In  the  year  1830  it  was  found  that  BOUVARD'S  tables, 
which  represented  the  motion  of  the  planet  well  during  the 
years  1820-25,  were  20"  in  error.  In  1840  the  error  was 
90",  and  in  1845  it  was  over  120." 

These  progressive  changes  attracted  the  attention  of 
astronomers  to  the  subject  of  the  theory  of  the  motion  of 
Uranus.  The  actual  discrepancy  (120")  in  1845  was  not  a 
quantity  large  in  itself.  Two  stars  of  the  magnitude  of 
Uranus,  and  separated  by  only  120",  would  be  seen  as  one 
to  the  unaided  eye.  It  was  on  account  of  its  systematic  and 
progressive  increase  that  suspicion  was  excited. 

Several  astronomers  attacked  the  problem  in  various 
ways.  The  elder  STRUVE,  at  Pulkova  in  Russia,  searched 


342  ASTRONOMY. 

for  a  new  planet  with  the  large  telescope  of  the  Imperial 
Observatory.  BESSEL,  at  Koenigsberg,  set  a  student  of  his 
own,  FLEMING,  to  make  a  new  comparison  of  observation 
with  theory,  in  order  to  furnish  data  for  a  new  determina- 
tion. ARAGO,  then  Director  of  the  Observatory  at  Paris, 
suggested  this  subject  in  1845  as  an  interesting  field  of 
mathematical  research  to  LE  VERRIER.  Mr.  J.  0.  ADAMS, 
a  student  in  Cambridge  University,  England,  had  become 
aware  of  the  problems  presented  by  the  anomalies  in  the 
motion  of  Uranus,  and  had  attacked  this  question  as  early 
as  1843. 

In  October,  1845,  ADAMS  communicated  to  the  As- 
tronomer Koyal  of  England  elements  of  a  new  planet  so 
situated  as  to  produce  the  perturbations  of  the  motion  of 
Uranus  which  had  actually  been  observed.  Such  a  predic- 
tion from  an  entirely  unknown  student,  as  ADAMS  then 
was,  did  not  carry  entire  conviction  with  it.  A  series  of 
accidents  prevented  the  unknown  planet  being  looked  for 
by  one  of  the  largest  telescopes  in  England,  and  so  the 
matter  apparently  dropped.  It  may  be  noted,  however, 
that  we  now  know  ADAMS'  elements  of  the  new  planet  to 
have  been  so  near  the  truth  that  if  it  had  been  really  looked 
for  by  the  powerful  telescope  which  afterward  discovered 
its  satellite,  it  could  scarcely  have  failed  of  detection. 

BESSEL'S  pupil  FLEMING  died  before  his  work  was  done, 
and  BESSEL'S  researches  were  temporarily  brought  to  an 
end.  STRUVE'S  search  was  unsuccessful.  LE  VERRIER, 
however,  continued  his  investigations,  and  in  the  most 
thorough  manner.  He  first  computed  anew  the  perturba- 
tions of  Uranus  produced  by  the  action  of  Jupiter  and 
Saturn.  Then  he  examined  the  nature  of  the  irregulari- 
ties observed.  These  showed  that  if  they  were  caused  by 
an  unknown  planet,  it  could  not  be  between  Saturn  and 
Uranus,  because  Saturn  would  have  been  more  affected 
than  was  the  case. 


THE  PLANET  NEPTUNE.  343 

If  the  new  planet  existed  at  all  it  was  outside  of  Uranus. 
In  the  summer  of  1846,  LE  VERRIER  obtained  complete 
elements  of  a  new  planet,  which  would  account  for  the 
observed  irregularities  in  the  motion  of  Uranus,  and  these 
were  published  in  France.  They  were  very  similar  to 
those  of  ADAMS,  and  this  striking  fact  renewed  the  interest 
in  ADAMS'  work.  It  was  determined  to  search  in  the 
heavens  for  the  planet  foretold  by  theory. 

Professor  CHALLIS,  the  Director  of  the  Observatory  of 
Cambridge,  England,  began  a  search  for  such  an  object,  and 
as  no  star-maps  were  at  hand  for  this  region  of  the  sky,  he 
commenced  by  mapping  the  surrounding  stars.  In  so 
doing  the  new  planet  was  actually  observed,  both  on  August 
4  and  12,  1846,  but  the  observations  remained  unreduced, 
and  the  planetary  nature  of  the  object  was  not  recognized 
till  afterwards. 

In  September  of  the  same  year  LE  VERRIER  wrote  to 
Dr.  GALLE,  then  Assistant  at  the  Observatory  of  Berlin, 
asking  him  to  search  for  the  new  planet,  and  directing  him 
to  the  place  where  it  should  be  found.  By  the  aid  of  an 
excellent  star-chart  of  this  region,  which  had  just  been 
completed,  the  new  planet  was  found  September  23,  1846. 

The  strict  rights  of  discovery  lay  with  LE  VERRIER,  but  ADAMS 
deserves  an  equal  share  in  the  honor  attached  to  this  most  brilliant 
achievement.  Indeed,  it  was  only  by  the  most  unfortunate  succession 
of  accidents  that  the  discovery  did  not  attach  to  Adams'  researches. 
One  thing  must  in  fairness  be  said,  and  that  is  that  the  results  of 
LE  VERRIER  were  reached  after  a  most  thorough  investigation  of  the 
whole  ground,  and  were  announced  with  an  entire  confidence  which, 
perhaps,  was  lacking  in  the  other  case. 

This  brilliant  discovery  created  even  more  enthusiasm 
than  the  discovery  of  Uranus,  as  it  was  by  an  exercise  of 
far  higher  intellectual  qualities  that  it  was  achieved.  It 
was  nothing  short  of  marvellous  that  a  mathematician  could 
say  to  an  observer  that  if  he  would  point  his  telescope  to  a 


344:  ASTRONOMY. 

certain  small  area,  he  would  find  within  it  a  major  planet 
hitherto  unknown.  Yet  so  it  was.  By  somewhat  similar 
processes  previously  unknown  companions  to  the  bright 
stars  Sirius  and  Procyon  have  been  predicted,  and  these 
companions  have  subsequently  been  discovered  with  the 
telescope. 


FIG.  188.— PERTURBATIONS  OP  Uranus  BY  A  PLANET  EXTERIOR 
TO  IT — Neptune. 

The  general  nature  of  the  disturbing  force  which  revealed  the  new 
planet  may  be  seen  by  Fig.  188,  which  shows  the  orbits  of  the  two 
planets,  and  their  respective  motions  between  1781  and  1840.  The 
inner  orbit  is  that  of  Uranus,  the  outer  one  that  of  Neptune.  The 
arrows  show  the  directions  of  the  attractive  force  of  Neptune. 

Our  knowledge  regarding  Neptune  is  mostly  confined  to 
a  few  numbers  representing  the  elements  of  its  motion. 
Its  mean  distance  is  more  than  2,775,000,000  miles;  its 
periodic  time  is  164.78  years;  its  apparent  diameter  is  2.6 
seconds,  corresponding  to  a  true  diameter  of  about  34,000 
miles.  Gravity  at  its  surface  is  about  nine  tenths  of  the 


CONSTITUTION  OF  THE  PLANETS.  345 

corresponding  terrestrial  surface  gravity.  Of  its  rotation 
and  physical  condition  nothing  is  known.  Its  color  is  a  pale 
greenish  blue.  It  is  attended  by  one  satellite,  which  was 
discovered  by  Mr.  LASSELL,  of  England,  in  1847.  The 
satellite  requires  a  telescope  of  twelve  inches'  aperture  or 
upward  to  be  well  seen.  It  is  not  unlikely  that  the  planet 
may  have  a  second  very  faint  satellite. 

38.  The  Physical  Constitution  of  the  Planets.— The  solar  system  is 
composed  of  three  groups  of  planets  differing  widely  in  their  char- 
acteristics. The  first  group  consists  of  Mercury,  Venus,  the  Earth, 
Mars  ;  the  second  group  is  the  asteroids  ;  the  third  consists  of  Ju- 
piter, Saturn,  Uranus,  and  Neptune.  The  diameters  of  the  first  group 
vary  from  3000  to  8000  miles,  their  periodic- times  are  less  than  two 
years,  their  masses  are  never  greater  than  5^^^  of  the  Sun's  mass, 
their  densities  are  from  3  to  5£  times  the  density  of  water.  The  Moon, 
the  satellite  of  the  Earth,  belongs  in  this  group.  Its  density  is  3.4 
times  the  density  of  water.  Two  planets  of  this  group —  Venus  and 
the  Earth — are  certainly  surrounded  by  atmospheres.  The  others 
probably  have  little  or  no  atmosphere.  The  planets  of  this  group 
were  named  by  ALEXANDER  VON  HUMBOLDT  terrestrial  planet*.  They 
are  in  some  respects  like  the  Earth.  At  any  rate,  all  of  them  are 
much  more  like  the  Earth  than  like  the  giant  planets  beyond  Mars. 

The  asteroids  are  quite  unique  among  the  planets.  Jupiter,  Saturn, 
Uranus,  Neptune  present  many  striking  resemblances.  They  are  of 
giant  size.  Their  diameters  vary  from  30,000  to  90,000  miles. 
Their  masses  are  relatively  large  (^^^^  to  y^^  of  the  Sun's  mass), 
their  densities  are  all  small  (none  greater  than  1£  times  the  density 
of  water).  At  least  two  of  them  have  a  very  short  period  of  rotation, 
and  all  of  them  have  a  high  reflecting  power.  Their  surfaces  are 
covered  with  clouds  and  there  is  good  reason  to  believe  that  one  of 
them — Jupiter — is  still  a  very  hot  body.  Very  likely  all  of  them 
consist  of  masses  of  molten  matter  surrounded  by  envelopes  of  vapor. 
This  view  is  further  strengthened  by  their  very  small  specific  grav- 
ity, which  can  be  accounted  for  by  supposing  that  the  liquid  interior 
is  nothing  more  than  a  comparatively  small  central  core,  and  that  the 
greater  part  of  the  bulk  of  each  planet  is  composed  of  vapor  of  small 
density.  Some  of  the  satellites  of  this  group  are  about  as  large  as 
Mars  or  Mercury. 

Finally  the  central  body  of  the  whole  system— the  Sun — is  im- 
mensely larger  than  all  the  planets  tak>  n  together;  it  is  very  hot ;  it 


346  ASTRONOMY. 

is  almost  or  entirely  gaseous  ;  its  density  is  less  than  1T47  the  density 
of  water — and  this  in  spite  of  the  immense  pressure  on  its  interior 
parts.  Mercury,  Mars,  the  Moon,  are  airless,  cold,  dense,  small. 
We  know  little  of  Venus  except  that  she  is  covered  with  clouds. 
Venus  may  be  more  like  the  Earth  than  any  other  planet.  The  aster- 
oids are  mere  fragments,  probably  all  airless  and  cold.  The  giant 
planets  are  (probably)  all  hot,  with  a  solid  or  liquid  nucleus  and  a 
deep  atmosphere.  And  at  the  end  of  the  series  comes  the  Sun,  hot, 
gaseous,  immensely  larger  than  the  planets. 

The  differences  between  these  different  bodies  are  chiefly  due  to 
temperature.  If  any  one  of  them  were  to  be  suddenly  raised  to  the 
Sun's  temperature  it  would  probably  be  a  miniature  Sun.  Each  of 
these  bodies  is  cooling  by  the  radiation  of  its  heat  into  space.  None 
of  the  heat  radiated  returns  to  the  body,  so  far  as  is  known.  The 
Sun  in  cooling  will  probably  become  a  body  somewhat  like  Jupiter. 
Jupiter  in  cooling  will  probably  become  a  body  somewhat  like  the 
Earth.  The  Earth  in  cooling  will  probably  become  a  body  somewhat 
like  the  Moon.  The  Moon  has  already  reached  its  permanent  state. 
Its  heat  has  gone;  it  has  no  atmosphere;  and  its  temperature  on  the 
side  turned  away  from  the  Sun  is  the  temperature  of  space  hundreds 
of  degrees  below  zero  Fahrenheit. 

The  temperature  of  any  planet  in  the  system  thus  depends,  in  an 
important  degree,  on  its  age.  It  depends  also  on  a  thousand  other 
circumstances— on  the  kind  of  matter  of  which  it  is  made  up,  on  its 
size,  etc.  When  we  come  to  consider  the  Nebular  Hypothesis  of 
KANT  and  LAPLACE,  which  is  an  attempt  to  explain  the  evolution  of 
the  solar  system,  these  facts  (and  others  not  here  explicitly  set  down) 
will  be  found  to  be  highly  significant. 


CHAPTEE  XX. 

METEORS. 

39.  Phenomena  of  Meteors  and  Shooting-stars. — Any 
one  who  watches  the  heavens  at  night  for  a  few  hours  will 
see  shooting-stars  or  meteors.  They  suddenly  appear  as 
bright  points  of  light,  move  along  an  arc  in'  the  sky  and 
then  disappear.  Large  meteors — aerolites — are  often  as 
bright  as  Venus  or  even  very  much  brighter;  they  are 
usually  followed  by  brilliant  trains ;  they  frequently  explode 
in  the  air,  like  rockets,  and  leave  clouds  of  meteoric  dust 
behind  them.  Sometimes  their  bursting  or  their  passage 
through  the  atmosphere  is  accompanied  by  an  audible  noise. 
Occasionally  fragments  of  the  aerolite  fall  to  the  Earth. 
Large  collections  of  such  fragments  are  preserved  in  our 
museums,  and  some  of  the  specimens  weigh  hundreds  of 
pounds.  Usually,  however,  they  are  much  smaller. 

Most  of  the  specimens  of  aerolites  aie  stones;  some  of 
them, are  nearly  pure  iron  alloyed  with  nickel,  etc. 

When  we  consider  that  the  aerolites  come  from  regions 
beyond  the  Earth  and  that  they  never  had  any  direct  con- 
nection with  it  before  their  fall  on  its  surface,  it  is  a  highly 
significant  fact  that  they  contain  no  chemical  elements  not 
found  on  the  Earth.  It  indicates  that  all  the  bodies  of  the 
solar  system  are  similar  in  constitution.  Moreover,  of  the 
seventy  or  more  elements  known  to  us  more  than  twenty 
have  been  found  in  meteoric  masses.  The  minerals  formed 
by  the  combination  of  the  elements  are  often  somewhat  dif- 
ferent in  the  aerolites  from  the  corresponding  minerals 
found  in  the  Earth's  crust,  which  seems  to  show  that  they 

347 


ASTRONOMY. 


FIG.  189. — THE  GREAT  CALIFORNIA  METEOR  OF  1894. 


METEORS.  349 

were  combined  under  quite  different  conditions  of  heat, 
pressure,  etc.  An  aerolite  is  a  little  planet  out  of  the 
celestial  spaces,  evident  to  our  sight,  it  may  be  to  our 
touch. 

Path  of  a  Meteor. — The  positions  of  a  meteor  can  be  observed 
by  referring  it  to  neighboring  stars — we  can  draw  its  path  on  a 
star-map,  and  note  the  time  of  its  appearance  or  bursting.  If  such 
observations  are  made  by  observers  at  different  stations  on  the 
Earth,  the  orbit  of  the  meteor  can  be  calculated.  It  is  found  that 
most  aerolites,  or  large  meteors,  were  moving  in  elliptic  orbits  about 
the  Sun  before  they  fell  into  the  sphere  of  the  Earth's  attraction. 
The  Earth,  of  course,  alters  such  an  orbit,  and  draws  the  body  down- 
wards into  the  atmosphere  with  a  high  velocity.  In  most  cases  it  is 
consumed — burned  up  completely — in  our  atmosphere.  Occasionally 
pieces  of  it  fall  to  the  ground,  as  has  been  said. 

Cause  of  the  Light  and  Heat  of  Meteors.— Why  do  meteors  burn 
with  so  great  an  evolution  of  light  on  reaching  our  atmosphere  ? 
To  answer  this  question  we  must  have  recourse  to  the  mechanical 
theory  of  heat.  Heat  is  a  vibratory  motion  in  the  particles  of  solid 
bodies  and  a  progressive  motion  in  those  of  gases.  The  more  rapid 
the  motion  the  warmer  the  body.  By  simply  blowing  air  against 
any  combustible  body  with  high  velocity  it  can  be  set  on  fire,  and,  if 
the  body  is  incombustible,  it  can  be  made  red-hot  and  finally  melted. 

Experiments  show  that  a  velocity  of  about  50  metres  (about  164 
feet)  per  second  corresponds  to  a  rise  of  temperature  of  one  degree 
Centigrade.  From  this  the  temperature  due  to  any  velocity  can  be 
calculated  on  the  principle  that  the  increase  of  temperature  is  pro- 
portional to  the  "energy"  of  the  particles,  which  again  is  propor- 
tional to  the  square  of  the  velocity.  A  velocity  of  500  metres  (about 
1640  feet)  per  second  corresponds  to  a  rise  of  100°  C.  above  the  actual 
temperature  of  the  air,  so  that  if  the  latter  was  at  the  freezing-point 
the  body  would  be  raised  to  the  temperature  of  boiling  water.  A 
velocity  of  1500  metres  (4921  feet,  about  twice  the  velocity  of  a 
cannon-ball)  per  second  would  produce  a  red  heat. 

The  Earth  moves  around  the  Sun  with  a  velocity  of  about  30,000 
metres  (18£  miles)  per  second;  consequently  if  it  met  a  body  at  rest 
the  concussion  between  the  latter  and  the  atmosphere  would  corre- 
spond to  a  temperature  of  more  than  300,000°.  This  would  instantly 
change  any  known  substance  from  a  solid  to  a  gaseous  form. 

It  must  be  remembered  that  these  enormous  temperatures  are 
potential .[joot  actual,  temperatures.  The  body  is  not  actually  raised 


350  ASTRONOMY. 

to  a  temperature  of  300,000°,  but  the  air  acts  upon  it  as  if  it  were 
suddenly  plunged  into  a  furnace  heated  to  this  temperature.  It  is 
rapidly  destroyed  just  as  if  it  were  in  such  a  furnace. 

The  potential  temperature  is  independent  of  the  density  of  the 
medium,  being  the  same  in  the  rarest  as  in  the  densest  atmosphere. 
But  the  actual  effect  on  the  body  is  not  so  great  in  a  rare  as  in  a 
dense  atmosphere.  Every  one  knows  that  he  can  hold  his  hand  for 
some  time  in  air  at  the  temperature  of  boiling  water.  The  rarer  the 
air  the  higher  the  temperature  the  hand  would  bear  without  injury. 
In  an  atmosphere  as  rare  as  ours  at  the  height  of  50  miles,  it  is  prob- 
able that  the  hand  could  be  held  for  an  indefinite  period,  though  its 
temperature  should  be  that  of  red-hot  iron ;  hence  the  meteor  is  not 
consumed  so  rapidly  as  if  it  struck  a  dense  atmosphere  with  a  like 
velocity.  In  the  latter  case  it  would  probably  disappear  like  a  flash 
of  lightning. 

The  amount  of  heat  evolved  is  measured  not  by  that  which  would 
result  from  the  combustion  of  the  body,  but  by  the  ms  viva  (energy 
of  motion)  which  the  body  loses  in  the  atmosphere.  The  student  of 
physics  knows  that  motion,  when  lost,  is  changed  into  a  definite 
amount  of  heat. 

The  amount  of  heat  which  is  equivalent  to  the  energy  of  motion 
of  a  pebble  having  a  velocity  of  20  miles  a  second  is  sufficient  to 
raise  about  1300  times  the  pebble's  weight  of  water  from  the  freezing 
to  the  boiling  point.  This  is  many  times  as  much  heat  as  could 
result  from  burning  pure  carbon. 

Meteoric  Phenomena. — Meteoric  phenomena  depend  upon  the  sub. 
stance  out  of  which  the  meteors  are  made  and  the  velocity  with 
which  they  move  in  the  atmosphere.  With  very  rare  exceptions, 
they  are  so  small  and  fusible  as  to  be  entirely  dissipated  in  the 
upper  regions  of  the  air.  On  rare  occasions  the  body  is  so  hard  and 
massive  as  to  reach  the  Earth  without  being  entirely  consumed. 
The  potential  heat  produced  by  its  passage  through  the  atmosphere 
is  expended  in  melting  and  destroying  its  outer  layers,  the  inner 
nucleus  remaining  unchanged.  When  a  meteor  first  strikes  the 
denser  portion  of  the  atmosphere,  the  resistance  becomes  so  great 
that  the  body  is  generally  broken  to  pieces.  A  single  large  aerolite 
may  produce  a  shower  of  small  meteoric  stones. 

Heights  of  Meteors. — Many  observations  have  been  made  to  deter- 
mine the  height  at  which  meteors  are  seen.  This  is  effected  by  two 
observers  stationing  themselves  several  miles  apart  and  mapping  out 
the  courses  of  such  meteors  as  they  can  observe. 

Meteors  and  shooting-stars  commonly  commence  to  be  visible  at  a 


METEORS.  351 

height  of  about  70  statute  miles.  The  separate  results  vary  widely, 
but  this  is  a  rough  average.  They  are  generally  dissipated  at  about 
half  this  height,  and  therefore  above  the  highest  atmosphere  which 
reflects  the  rays  of  the  Sun.  The  Earth's  atmosphere  must,  then, 
extend  at  least  as  high  as  70  miles. 

While  there  are  few  aerolites  or  large  meteors,  there  are 
millions  of  the  smaller  sort — shooting-stars.  A  single 
observer  will  see,  on  the  average,  from  four  to  eight  every 
hour.  If  the  whole  sky  is  watched  at  any  one  place  on  the 
Earth  from  30  to  60  are  visible  every  hour.  They  fill 
space  like  particles  of  dust,  only  these  particles  of  the 
dust  of  space  are,  on  the  average,  about  200  miles  apart. 
The  Earth  sweeps  along  in  its  orbit  at  the  rate  of  18J  miles 
per  second  and  in  its  daily  journey  of  some  1,600,000  miles 
it  meets,  or  is  overtaken  by  millions  of  these  bodies.  From 
10  to  15  millions  of  meteors  fall  into  the  Earth's  atmos- 
phere every  day.  The  mass  of  the  single  meteors  is  ex- 
tremely small — several  thousands  of  them  being  required 
to  make  up  a  pound's  weight.  If  each  meteor  has  a  mass 
of  one  grain  the  Earth  is  growing  heavier  daily  by  about  a 
ton.  Theoretically  the  Earth  is  daily  receiving  heat  by  the 
fall  of  meteorites,  also;  but  calculation  shows  that  the  Sun 
sends  us  ten  times  as  much  heat  in  a  second  as  is  received 
from  meteors  in  a  year;  so  that  there  is  no  noteworthy 
effect  from  this  cause. 

Meteoric  Showers. — Shooting-stars  may  be  seen  by  a 
careful  observer  on  almost  any  clear  night.  In  general, 
not  more  than  half-a-dozen  will  be  seen  in  an  hour,  and 
these  are  usually  so  minute  as  hardly  to  attract  notice. 
But  they  sometimes  fall  in  great  numbers  as  a  meteoric 
shower.  On  rare  occasions  the  shower  has  been  so  striking 
as  to  fill  the  beholders  with  terror.  Ancient  and  mediaeval 
records  contain  many  accounts  of  such  phenomena. 

One  shower  of  this  class  occurs  at  an  interval  of  about  a 
third  of  a  century.  It  was  observed  by  HUMBOLDT,  on  the 


352  ASTRONOMY. 

Andes,  on  the  night  of  November  12,  1799,  for  instance, 
and  often  before  that  time.  A  great  shower  was  seen  in 
this  country  in  1833.  On  the  night  of  November  13,  1866, 
a  remarkable  shower  was  seen  in  Europe,  while  on  the 
corresponding  night  of  the  year  following  it  was  again  seen 
in  this  country,  and,  in  fact,  was  repeated  for  two  or  three 
years,  gradually  dying  away,  as  it  were.  This  great  shower 
will  appear  in  1899,  once  more. 

The  occurrence  of  a  shower  of  meteors  evidently  shows 
that  the  Earth  encounters  a  swarm  of  such  bodies  moving 
together  in  space.  The  recurrence  at  the  same  time  of  the 
year  (when  the  Earth  is  in  the  same  point  of  its  orbit) 
shows  that  the  Earth  meets  the  swarm  at  the  same  point  in 
space  in  successive  years.  All  the  meteors  of  the  swarm 
must  be  moving  in  the  same  direction  in  space  or  else  they 
would  soon  be  widely  scattered. 

Radiant  Point. — Suppose  that,  during  a  meteoric  shower,  we  mark 
the  path  of  each  meteor  on  a  star-map,  as  in  figure  190.  If  we  con- 
tinue the  observed  paths  backward  in  a  straight  line,  we  shall  find 
that  they  all  meet  near  one  and  the  same  point  of  the  celestial  sphere; 
that  is,  they  move  as  if  they  all  radiated  from  this  point.  The  latter 
is,  therefore,  called  the  radiant  point.  In  the  figure  the  lines  do  not 
all  pass  accurately  through  the  same  point  owing  to  the  unavoidable 
errors  made  in  marking  out  the  path. 

It  is  found  that  the  radiant  point  is  always  in  the  same  position 
among  the  stars,  wherever  the  observer  may  be  situated,  and  that, 
as  the  stars  apparently  move  toward  the  west,  the  radiant  point  moves 
with  them. 

The  existence  of  a  radiant  point  proves  that  the  meteors  that  strike 
the  Earth  during  a  shower  are  all  moving  in  the  same  direction. 
Their  motions  will  all  be  parallel  ;  hence  when  the  bodies  strike  our 
atmosphere  the  paths  described  by  them  in  their  passage  will  all  be 
parallel  straight  lines.  A  straight  line  in  space  seen  by  an  observer 
is  projected  as  a  great  circle  of  the  celestial  sphere,  with  the 
observer  at  its  centre.  If  we  draw  a  line  from  the  observer  parallel 
to  the  paths  of  the  meteors,  the  direction  of  that  line  intersects  the 
celestial  sphere  in  a  point  through  which  all  the  meteor-paths  will 
seem  to  pass. 


METEORS. 


353 


Orbits  of  Showers  of  Meteors.— The  position  of  the  radiant  point  in- 
dicates the  direction  in  which  the  meteors  move  relatively  to  the 


FIG.  190.— THE  RADIANT  POINT  OP  A  METEORIC  SHOWER. 


Earth.    If  we  also  knew  the  velocity  with  which  they  are  really  mov- 
ing in  space,  we  could  make  allowance  for  the  motion  of  the  Earth, 


354  ASTRONOMY. 

and  thus  determine  the  direction  of  their  actual  motion  in  space,  and 
determine  the  orbit  of  the  swarm  around  the  Sun. 

The  radiant  point  of  the  shower  of  August  10  (Perseids)  is  R.A. 
3h  4m  Decl.  -f-  57° ;  of  the  shower  of  November  13  (Leonids)  R.A.  10h 
Om,  Decl.  +  23° ;  of  the  shower  of  November  26  (Andromedes}  R.A. 
lh  41m,  Decl.  -)-  43°.  The  student  should  observe  these  showers. 

Relations  of  Meteors  and  Comets.— The  velocity  of  the 
meteors  in  space  does  not  admit  of  being  determined  from 
observation  of  the  meteors  themselves.  It  is  necessary  to 
determine  their  velocity  in  the  orbit  from  the  periodic-time 
of  the  swarm  about  the  Sun.  The  orbit  of  the  swarm 
giving  the  33-year  shower  was  calculated  shortly  after  the 
great  shower  of  1866  with  the  results  that  follow: 

Period  of  revolution 33.25  years 

Eccentricity  of  orbit 0.9044 

Least  distance  from  the  sun. .  . .     0.9890 

Inclination  of  orbit 165°  19' 

Longitude  of  the  node 51°  18' 

Position  of  the  perihelion (near  the]  node) 

The  orbit  of  the  meteor-swarm  presents  an  extraordinary 
likeness  to  the  orbit  of  a  periodic  comet  discovered  by 
TEMPEL.  The  elements  of  the  comet's  orbit  are: 

Period  of  revolution 33.18  years. 

Eccentricity  of  orbit 0.9054 

Least  distance  from  the  sun 0.9765 

Inclination  of  orbit 162°  42' 

Longitude  of  the  node 51°  26' 

Longitude  of  the  perihelion 42°  24' 

If  the  two  orbits  are  compared,  the  result  is  evident. 
The  swarm  of  meteors  which  causes  the  November  shoivers 
moves  in  the  same  orbit  with  TEMPEL'S  comet. 

The  comet  passed  its  perihelion  in  January,  1866.  The 
shower  was  not  visible  until  the  following  November. 


METEORS.  355 

Therefore,  the  swarm  which  produced  the  showers  followed 
after  TEMPEL'S  comet,  moving  in  the  same  orbit  with  it. 
The  recurrence  of  the  phenomenon  every  33  years  was 
traced  backward  in  historical  records  and  it  was  shown  that 
for  centuries  this  swarm  had  been  revolving  about  the  Sun. 
The  swarm  is  stretched  out  in  a  long  mass  and  the  Earth 
crosses  the  orbit  in  November  of  every  year.  The  Earth 
finds  the  swarm  in  its  path  every  33  years.  The  radiant 
point  of  the  November  shower  is  in  the  constellation  Leo 
and  hence  these  meteors  are  called  Leonids.  The  August 
meteors  radiate  from  Perseus  and  are  called  Perseids.  The 
relation  between  comets  and  meteors  suggested  the  question 
whether  a  similar  connection  might  not  be  found  between 
other  comets  and  other  meteoric  showers. 

Other  Showers  of  Meteors. — Although  the  November  showers  (which 
occur  about  November  14)  are  the  only  ones  so  brilliant  as  to  strike 
the  ordinary  eye,  it  has  long  been  known  that  there  are  other  nights 
of  the  year  (notably  August  10)  in  which  more  shooting-stars  than 
usual  are  seen,  and  in  which  the  large  majority  radiate  from  one 
point  of  the  heavens.  They  also  arise  from  swarms  of  ineteoroids 
moving  together  around  the  Sun. 

The  honor  of  the  discovery  of  this  remarkable  and  unexpected 
relation  between  meteors  and  comets  is  shared  between  several 
astronomers.  Professors  OLMSTED  and  TWINING  of  Yale  College 
were  the  first  to  show  that  meteors  were  extra-terrestrial  bodies  re- 
volving in  swarms  about  the  Sun.  Professors  ERMAN  of  Germany, 
LE  VERRIER  of  France,  ADAMS  of  England,  SCHTAPARELLI  of  Italy 
and  particularly  Professor  NEWTON  of  Yale  College  developed  the 
whole  subject. 

Many  meteor-swarms  revolve  in  the  same  orbits  with 
comets.  In  some  cases  the  swarms  follow  the  comet  in  a 
more  or  less  compact  mass.  In  others  the  meteors  are 
scattered  all  around  the  orbit.  If  a  comet,  originally,  is 
nothing  but  a  close  cluster  of  meteors  it  will  partially  break 
up  into  its  parts  under  the  influence  of  planetary  attractions 
(perturbations)  and  especially  at  every  one  of  its  perihelion 
passages.  The  longer  a  comet  has  been  in  the  solar  system 


356  ASTRONOMY. 

the  more  the  meteors  will  be  spread  ont  along  its  orbit. 
But  it  is  by  no  means  certain  that  comets  are,  in  the  first 
place,  only  aggregations  of  meteors,  so  that  it  can  only  be 
said  that  there  is,  certainly,  a  very  close  connection  between 
meteors  and  comets,  and  that  it  is  likely  that  certain 
meteor-swarms  are  no  more  than  the  debris  of  comets. 
Beside  the  meteors  known  to  be  connected  with  comets 
there  are  millions  upon  millions  of  others  scattered  through 
space. 

The  Zodiacal  Light. — If  we  observe  the  western  sky  during  the 
winter  or  spring  months,  about  the  end  of  the  evening  twilight,  we 
shall  see  a  stream  of  faint  light,  a  little  like  the  Milky  Way,  rising 
obliquely  from  the  west,  and  directed  along  the  ecliptic  toward  a 
point  southwest  from  the  zenith.  This  is  called  the  Zodiacal  Light. 
It  may  also  be  seen  in  the  east  before  daylight  in  the  morning  during 
the  autumn  months,  and  can  be  traced  all  the  way  across  the  heavens. 
A  brighter  mass  opposite  to  the  Sun's  place  is  called  the  Gegenschein. 
The  Zodiacal  Light  is  probably  due  to  solar  light  reflected  from  an 
extremely  thin  cloud  either  of  meteors  or  of  semi-gaseous  matter  like 
that  composing  the  tail  of  a  comet,  spread  all  around  the  Sun  inside 
the  Earth's  orbit.  Its  spectrum  is  probably  that  of  reflected  sunlight, 
a  result  which  gives  color  to  the  theory  that  it  arises  from  a  cloud  of 
meteors  revolving  round  the  Sun.  The  student  should  trace  out  the 
Zodiacal  Light  in  the  sky. 


CHAPTER   XXI. 

COMETS. 

40.  Aspect  of  Comets. — Comets  are  distinguished  from 
the  planets  both  by  their  aspects  and  their  motions.  Only 
a  few  comets  belong  permanently  to  the  solar  system  (see 
Table  IV,  p.  279).  Most  of  them  are  mere  visitors.  They 
enter  the  system,  go  round  the  Sun  once,  and  then  leave  it 
forever. 

The  nucleus  of  a  comet  is,  to  the  naked  eye,  a  point  of 
light  resembling  a  star  or  planet.  Viewed  in  a  telescope, 
it  generally  has  a  small  disk,  but  shades  off  so  gradually 
that  it  is  difficult  to  estimate  its  magnitude.  In  large 
comets  it  is  sometimes  several  hundred  miles  in  diameter. 

The  nucleus  is  always  surrounded  by  a  mass  of  foggy 
light,  which  is  called  the  coma.  To  the  naked  eye  the 
nucleus  and  coma  together  look  like  a  star  seen  through  a 
mass  of  thin  fog,  which  surrounds  it  with  a  sort  of  halo. 
The  nucleus  and  coma  together  are  generally  called  the 
head  of  the  comet.  The  head  of  the  great  comet  of  1858 
was  250,000  miles  in  diameter. 

The  tail  of  the  comet  is  a  continuation  of  the  coma, 
extending  out  to  a  great  distance,  and  usually  directed 
away  from  the  Sun.  It  has  the  appearance  of  a  stream  of 
milky  light,  which  grows  fainter  and  broader  as  it  recedes 
from  the  head.  The  length  of  the  tail  varies  from  2°  or  3° 
to  90°  or  more.  The  tail  of  the  great  comet  of  1858  was 
45,000,000  miles  in  length  and  10,000,000  miles  in  breadth. 
All  that  area  was  filled  with  matter  sufficiently  condensed 
to  send  light  to  the  Earth  and  to  appear  as  a  continuous 

357 


358 


ASTRONOMY. 


FIG.  191.— THE  GREAT  COMET  OP  1858. 


COMETS.  359 

sheet.  The  mass  of  comets  is  extremely  small,  so  small 
that  no  comet  has  yet  been  observed  to  produce  perturba- 
tions in  the  motion  of  any  planet.  It  is  to  be  remembered 
that  we  do  not  see  the  tail  of  a  comet  in  its  true  shape,  but 
only  its  projection  on  the  celestial  sphere,  and  it  is  further- 
more to  be  noted  that  the  tail  is  not  the  debris  of  the  comet 
left  behind  the  comet  in  its  motion.  The  tail  of  a  comet 
is  behind  the  nucleus  as  the  comet  approaches  the  Sun,  but 
it  precedes  the  nucleus  as  the  comet  moves  away  from  the 
Sun.  The  vapors  that  arise  from  the  nucleus,  owing  chiefly 
to  the  Sun's  heat,  are  repelled  by  the  Sun — driven  away 
from  him  probably  by  electric  repulsion.  The  nucleus  it- 
self is  always  attracted  and  performs  its  revolution  about 
the  Sun  in  obedience  to  the  attraction  of  gravitation. 


FIG.  192.— TELESCOPIC  COMET         FIG.  193. — TELESCOPIC  COMET 
WITHOUT   A    NUCLEUS   AND  WITH  A  NUCLEUS,  BUT  WITH- 

WITHOUT  A  TAIL.  OUT  A  TAIL. 

When  large  comets  are  studied  with  a  telescope,  it  is 
found  that  they  are  subject  to  extraordinary  changes.  To 
understand  these  changes,  we  must  begin  by  saying  that 
comets  do  not,  like  the  planets,  revolve  around  the  Sun  in 
nearly  circular  orbits,  but  in  orbits  always  so  elongated  that 
the  comet  is  visible  in  only  a  very  small  part  of  its  course 
(see  Figs.  195,  196,  197) — namely,  in  that  part  of  its  orbit 
near  the  Sun  (and  Earth). 


£60  ASTRONOMY. 

The  Vaporous  Envelopes. — If  a  comet  is  very  small,  it  may  undergo 
no  changes  of  aspect  during  its  entire  course.  If  it  is  an  unusually 
bright  one,  a  bow  surrounding  the  nucleus  on  the  side  toward  the  Sun 
will  develop  as  the  comet  approaches  the  Sun.  (a,  Fig.  194.)  This 
bow  will  gradually  rise  and  spread  out  on  all  sides,  finally  assuming 
the  form  of  a  semicircle  having  the  nucleus  in  its  centre,  or,  to 
speak  with  more  precision,  the  form  of  a  parabola  having  the  nucleus 
near  its  focus.  The  two  ends  of  this  parabola  will  extend  out  further 
and  further  so  as  to  form  a  part  of  the  tail,  and  finally  be  joined  to  it. 
Other  bows  will  successively  form  around  the  nucleus,  all  slowly 
rising  from  it  like  clouds  of  vapor  (Fig.  194). 


FIG.  194. — FOKMATION  OF  ENVELOPES. 

These  distinct  vaporous  masses  are  called  the  envelopes  :  they 
shade  off  gradually  into  the  coma  so  as  to  be  with  difficulty  distin- 
guished from  it.  The  appearances  are  apparently  caused  by  masses 
of  vapor  streaming  up  from  that  side  of  the  nucleus  nearest  the  Sun 
(and  therefore  hottest)  and  gradually  spreading  around  the  comet  on 
each  side  as  if  repelled  by  the  Sun.  The  form  of  the  bow  is,  of 
course,  not  the  real  form  of  the  envelopes,  but  only  the  apparent  one 
in  which  we  see  them  projected  against  the  background  of  the  sky. 

Perhaps  their  forms  can  be  best  imagined  by  supposing  the  Sun 
to  be  directly  above  the  comet  (see  Fig.  194)  and  a  fountain,  throwing 
a  vapor  horizontally  on  all  sides,  to  be  built  upon  that  part  of  the 
comet  which  is  uppermost.  Such  a  fountain  would  throw  its  vapor 
in  the  .form  of  a  sheet,  falling  on  all  sides  of  the  cometic  nucleus, 
but  not  touching  it.  Two  or  three  vapor  surfaces  of  this  kind  are 
sometimes  seen  around  the  comet,  the  outer  one  enclosing  each  of 
the  inner  ones,  but  no  two  touching  each  other. 

The  tail  also  develops  rapidly  as  the  comet  draws  near  to  the  Sun, 
and  sometimes  several  tails  are  developed.  The  principal  tail  is 
directed  away  from  the  Sun,  as  if  under  electric  repulsion. 


COMETS.  361 

The  Constitution  of  Comets. — To  tell  exactly  what  a  comet  is,  we 
should  be  able  to  show  how  all  the  phenomena  it  presents  would 
follow  from  the  properties  of  matter,  as  we  learn  them  at  the  surface 
of  the  Earth.  This,  however,  no  one  has  been  able  to  do,  many  of 
the  phenomena  being  such  as  we  should  not  expect  from  the  known 
constitution  of  matter.  All  we  can  do,  therefore,  is  to  present  the 
principal  characteristics  of  comets,  as  shown  by  observation,  and  to 
explain  what  is  wanting  to  reconcile  these  characteristics  with  the 
known  properties  of  matter. 

In  the  first  place,  all  comets  which  have  been  examined  with  the 
spectroscope  show  a  spectrum  which  indicates  that  the  comets  are 
principally  made  up  of  gases  mostly  compounds  of  carbon  and 
hydrogen.  Sodium  and  several  other  substances  are  often  found. 
Part  of  the  comet's  light  is  undoubtedly  reflected  sunlight. 

It  is,  at  first  sight,  difficult  to  comprehend  how  a  mass  of  gas  of 
extreme  tenuity  can  move  in  a  fixed  orbit  just  as  if  it  were  a  solid 
planetary  mass.  The  difficulty  vanishes  when  we  remember  that  the 
spaces  in  which  comets  move  are  practically  empty — as  empty  as 
the  vacuum  of  an  air-pump.  In  such  a  vacuum  a  feather  falls  as 
freely  and  as  rapidly  as  a  block  of  metal. 

The  Orbits  of  Comets.— Previous  to  the  time  of  NEWTON  only  bright 
comets  had  been  observed  and  nothing  WHS  known  of  their  actual  mo- 
tions, except  that  no  one  of  them  moved  around  the  Sun  in  an  ellipse 
as  the  planets  moved.  NEWTON  found  that  a  body  moving  under  the 
attraction  of  the  Sun  might  move  in  anyone  of  the  three  "conic 
sections,"  the  ellipse,  parabola,  or  hyperbola.  Bodies  moving  in  an 
ellipse,  as  the  planets,  complete  their  orbits  at  regular  intervals  of 
time  over  and  over  again.  A  body  moving  in  a  parabola  or  an  hyper- 
bola never  returns  to  the  Sun  after  once  passing  it,  but  moves  away 
from  it  forever.  Most  comets  move  in  parabolic  orbits,  and  therefore 
a  proach  the  Sun  but  once  during  their  whole  existence  (Fig.  195). 

A  few  comets  revolve  around  the  Sun  in  elliptic  orbits,  which  differ 
from  those  of  the  planets  only  in  being  much  more  eccentric.  (See 
p.  279.)  But  nearly  all  comets  move  about  the  Sun  in  orbits  which 
we  are  unable  to  distinguish  from  parabolas,  though  it  is  possible 
that  some  of  them  may  be  extremely  elongated  ellipses.  It  is  note- 
worthy that  the  orbits  of  comets  are  inclined  at  all  angles  to  the 
ecliptic  and  that  their  directions  of  motion  are  often  retrograde.  In 
these  respects  they  differ  widely  from  the  planets. 

In  the  last  chapter  it  was  shown  that  swarms  of  minute  particles, 
small  meteors,  accompany  certain  comets  in  their  orbits.  This  is 
probably  true  of  all  comets.  We  can  only  regard  such  meteors  as 


362  ASTRONOMY. 

fragments  or  debris  of  the  comet.  On  this  theory  a  telescopic  comet 
which  has  no  nucleus  is  simply  a  cloud  of  these  minute  bodies.  Per- 
haps each  one  of  the  minute  particles  has  a  little  envelope  of  gases 
about  it.  The  nucleus  of  the  brighter  comets  may  either  be  a  more 
condensed  mass  of  such  bodies  or  it  may  be  a  solid  or  liquid  body 
itself. 

If  the  student  has  difficulty  in  reconciling  this  theory  of  detached 
particles  with  the  view  already  presented,  that  the  envelopes  from 
which  the  tail  of  the  comet  is  formed  consists  of  layers  of  vapor,  he 
must  remember  that  vaporous  masses,  such  as  clouds,  fog,  and 


FIG.  195  —ELLIPTIC  AND  PARABOLIC  ORBITS. 

smoke,  are  in  fact  composed  of  minute  and  separate  particles  of  water, 
carbon  and  so  forth. 

The  gases  shut  up  in  the  cavities  of  meteoric  stones  have  been 
spectroscopioally  examined,  and  they  show  the  characteristic  comet 
spectrum.  This  gives  a  new  proof  of  the  connection  between  comets 
and  meteors. 

Formation  of  the  Comet's  Tail. — The  tail  of  the  comet  is  not  a  per- 
manent appendage,  but  is  composed  of  masses  of  vapor  which  ascend 
from  the  nucleus,  and  afterwards  move  away  from  the  Sun.  The 


COMETS.  363 

tail  which  we  see  on  one  evening  is  not  absolutely  the  same  we  saw 
the  evening  before.  A  portion  of  the  latter  has  been  dissipated, 
while  new  matter  has  taken  its  place,  as  with  the  stream  of  smoke 
from  a  steamship.  It  is  an  observed  fact  that  the  vapor  which  rises 
from  the  nucleus  of  a  comet  is  repelled  by  the  Sun  instead  of  being 
attracted  toward  it,  as  larger  masses  of  matter  are  ;  as  indeed  the 
nucleus  itself  is. 

No  adequate  expl  nation  of  this  repulsive  force  has  yet  been  given. 
It  is  probably  electrical. 


FIG.  196.  — OKBTT  OF  HAT.LEY'S  COMET. 

Periodic  Comets. — The  first  discovery  of  the  periodicity  of  a  comet 
was  made  by  HALI.KY  in  connection  with  the  great  comet  of  1682. 
This  comet  moves  in  an  immense  elliptic  orbit  with  a  periodic  time 
of  76  years.  HALLEY  predicted  that  it  would  return  in  1758.  CLAI- 
RATJT,  a  French  astronomer,  worked  out  its  orbit  by  NEWTON'S 
methods,  and  the  comet  returned,  obedient  to  law,  on  Christmas 
day,  1758.  (See  Fig.  196.) 

Gravitation  was  thus,  for  the  first  time,  shown  to  rule  the  erratic 
motions  of  comets  as  well  as  the  orderly  revolutions  of  the  planets. 

The  figure  shows  the  very  eccentric  orbit  of  HALLEY'S  comet  and 
the  nearly  circular  orbits  of  the  four  outer  planets.  It  attained  its 
greatest  distance  from  the  Sun,  far  beyond  the  orbit  of  Neptune, 
about  the  year  1873,  and  then  commenced  its  return  journey.  The 
figure  also  shows  the  position  of  the  comet  in  1874.  It  will  return 
to  perihelion  again  in  the  year  1910. 


364 


ASTRONOMY. 


Orbit  of  a  Parabolic  Comet.  —Figure  197  shows  the  orbit  of  a  comet 
discovered  by  PERRINE  at  the  Lick  Observatory  on  November  17, 
1895.  The  places  of  the  comet  in  its  parabolic  orbit  are  marked  for 
November  20  and  subsequent  dates.  The  places  of  the  Earth  in  its 
orbit  are  marked  for  the  same  dates.  Lines  joining  the  correspond- 


\ 


5. 


FIG.  197. — THE  ORBIT  OF  COMET  0.  1895,  AND  THE  ORBIT  OF 
THE  EARTH,  DRAWN  TO  SCALE.  THE  SUN  is  AT  THE  CENTRE 
OF  THE  DIAGRAM. 


ing  dates  in  the  two  orbits  will  show  the  direction  in  which  the 
comet  was  seen  from  the  Earth.  A  line  shows  the  direction  of  the 
Vernal  Equinox.  The  plane  of  the  paper  is  the  plane  of  the  Eclip- 
tic. All  that  part  of  the  comet's  orbit  which  is  drawn  full  is  north 
of  the  Ecliptic;  the  dotted  portion  is  south  of  it.  The  line  of  nodes 


COMETS. 


365 


of  the  comet's  orbit  is  marked  on  the  diagram.  The  comet  was 
nearest  to  the  Sun  (at  perihelion)  on  December  18,  when  its  dis- 
tance was  0.19  (the  Earth's  distance  =  1.00).  The  positions  of  the 
comet  were 


Nov.  20 

R.  A.  208° 

Decl.  -  0° 

24 

211° 

-  3° 

28 

214° 

-  5° 

Dec.  2 

219° 

-  10° 

10 

286° 

-  22° 

18 

274° 

-  31° 

26 

287° 

-  23° 

Remarkable   Comets. — In  former  years  bright  comets 
were  objects   of   great   dread.      They   were  supposed   to 


DEB 

ERN  DROHT 
BOESE  SACHET 
TRAV". 
GOTT 


FIG.  198. — MEDAL  OF  THE  GREAT  COMET  OP  1680-81. 

presage  the  fall  of  empires,  the  death  of  monarchs,  the 
approach  of  earthquakes,  wars,  pestilence,  and  every  other 
calamity  that  could  afflict  mankind.  In  showing  the  entire 
groundlessness  of  such  fears,  science  has  rendered  one  of 
its  greatest  benefits  to  mankind. 

The  number  of  comets  visible  to  the  naked  eye,  so  far  as 
recorded,  has  generally  ranged  from  twenty  to  forty  in  a 
century.  Only  a  few  of  these,  however,  have  been  so 
bright  as  to  excite  universal  notice. 

In  1456  the  comet,  afterwards  known  as  HALLEY'S, 
appeared  when  the  Turks  were  making  war  on  Christen- 
dom, and  caused  such  terror  that  Pope  CALIXTUS  IIJ 


366  ASTRONOMY. 

ordered  prayers  to  be  offered  in  the  churches  for  protection 
against  it.  This  is  the  origin  of  the  popular  fable  that  the 
Pope  once  excommunicated  a  comet. 

Comet  of  1680.— One  of  the  most  remarkable  of  the  brilliant  comets 
is  that  of  1680.  It  inspired  such  terror  that  a  medal  was  struck  to 
quiet  popular  apprehension.  A  free  translation  of  the  inscription  is  : 
"The  star  threatens  evil  things;  trust  only  !  God  will  turn  them 
to  good."*  This  comet  is  especially  remarkable  in  the  history  of 
Astronomy  because  NEWTON  calculated  its  orbit,  and  showed  that  it 
moved  around  the  Sun  obedient  to  the  law  of  gravitation. 

Great  Comet  of  1811. — It  has  a  period  of  over  3000  years,  and  its 
aphelion  distance  is  about  40,000,000,000  miles. 

Great  Comet  of  1843.  — It  was  visible  in  full  daylight  close  to  the  Sun. 
At  perihelion  it  passed  nearer  the  Sun  than  any  other  body  has 
ever  been  known  to  pass,  the  least  distance  being  only  about 
one  fifth  of  the  Sun's  semidiaineter.  With  a  very  slight  change  of 
its  original  motion,  it  would  have  actually  fallen  into  the  Sun,  and 
become  a  part  of  it. 

Great  Comet  of  1858. — It  is  frequently  called  DONATI'S  comet  from 
the  name  of  its  discoverer.  It  was  visible  for  about  nine  months  and 
was  thoroughly  studied  by  many  astronomers,  particularly  by  BOND  at 
Harvard  College.  At  its  greatest  brilliancy  its  tail  was  40°  in  length 
and  10°  in  bread  that  its  outer  end,  about  45,000,000  and  10,000,000 
miles  in  real  (no  perspective)  dimensions.  Its  period  is  1950  years. 
(See  Fig.  191.) 

Great  Comet  of  1882.— It  was  visible  in  full  daylight  at  its  bright- 
est, and  it  was  seen  with  the  telescope  until  it  actually  appeared  to 
touch  the  Sun's  disk.  It  passed  across  the  face  of  the  Sun  (half  a 
degree)  in  less  than  fifteen  minutes,  with  the  enormous  velocity  of 
more  than  300  miles  per  second.  Its  least  distance  from  the  surface 
of  the  Sun  was  less  than  300,000  miles,  so  that  it  passed  through  the 
denser  portions  of  the  Sun's  Corona. 

The  orbit  of  this  comet  has  been  calculated  from  observations 
taken  before  its  perihelion  passage,  and  also  from  observations  taken 
after  it.  If  the  Corona  had  had  any  effect  on  the  comet's  motion 
these  two  orbits  would  have  differed  ;  but  they  do  not  differ  ;  they 


*Tho  student  should  notice  the  care  which  the  author  of  the  inscription  has 
taken  to  make  it  consolatory,  to  make  it  rhyme,  and  to  give  implicitly  the 
year  of  the  comet  by  writing  certain  Roman  numerals  larger  than  the  other 
letters. 


COMETS.  367 

agree  exactly.  This  shows  of  how  rare  suhstances  the  Corona  is 
made  up. 

The  periodic-time  of  this  comet  is  about  840  years  and  its  orbit 
is  the  same  curve  in  space  as  the  orbits  of  the  comets  of  1668,  1843 
and  1880  and  1887.  But  the  comets  themselves  are  different  bodies. 
The  comet  of  1882  and  that  of  1880  cannot  possibly  be  the  same, 
body.  They  travel  in  the  same  path,  however,  and  belong  to  the 
same  family  of  comets. 

Observations  of  comets  made  at  the  Lick  Observatory  and  elsewhere 
have  shown  that  comets  sometimes  break  up  into  fragments  which 
thereafter  travel  in  similar  paths  one  behind  the  other.  Pho- 
tographs of  comets  sometimes  actually  show  the  formation  of  com- 
panion comets  left  behind  or  rejected  by  the  main  comet.  From 
these  photographs  it  appears  that  the  head  of  a  comet  sends  out 
enormous  quantities  of  matter  to  form  the  tail ,  so  that  the  material 
that  forms  it  on  one  day  may  not  be  and  probably  is  not  the  same 
material  that  formed  the  tail  of  a  few  days  previous.  The  observa- 
tions and  photographs  referred  to  have  opened  a  new  field  for  investi- 
gation, and  it  is  likely  that  very  many  important  questions  as  to  the 
constitution  of  comets  will  be  settled  when  the  next  bright  cornet 
appears. 

Encke's  Comet  and  the  Resisting  Medium. — The  period  of  this 
comet  is  between  three  and  four  years.  Viewed  with  a  telescope,  it 
appears  simply  as  a  mass  of  foggy  light.  Under  the  most  favorable 
circumstances,  it  is  just  visible  to  the  naked  eye.  The  circumstance 
that  has  lent  most  interest  to  this  comet  is  that  observations  ex- 
tended over  many  years  indicate  that  it  is  gradually  approaching  the 
Sun. 

ENCKE  attributed  this  change  in  its  orbit  to  the  existence  in  space 
of  a  resisting  medium,  so  rare  as  to  have  no  appreciable  effect  upon 
the  motion  of  the  planets,  and  felt  only  by  bodies  of  extreme  tenuity, 
like  the  telescopic  comets.  The  approach  of  the  comet  to  the  Sun  is 
shown  by  a  gradual  diminution  of  the  period  of  revolution. 

If  the  change  in  the  period  of  this  comet  were  actually  due  to  the 
causes  which  ENCKE  supposed,  then  other  faint  comets  of  the  same 
kind  ought  to  be  subject  to  a  similar  influence.  But  the  investiga- 
tions which  have  been  made  in  recent  times  on  these  bodies  show  no 
deviations  of  the  kind.  It  might,  therefore,  be  concluded  that  the 
change  in  the  period  of  ENCKE'S  comet  must  be  due  to  some  other 
cause.  There  is,  however,  one  circumstance  which  leaves  us  in 
doubt. 

ENCKE'S  comet  passes  nearer  the  Sun  than  any  other  comet  of 


368  ASTRONOMY. 

short  period  which  has  been  observed  with  sufficient  care  to  decide 
the  question.  It  may,  therefore,  be  supposed  that  the  resisting 
medium,  whatever  it  may  be,  is  densest  near  the  Sun,  and  does  not 
extend  out  far  enough  for  the  other  comets  to  meet  it.  The  question 
is  one  very  difficult  to  settle.  The  fact  is  that  all  comets  exhibit 
slight  anomalies  in  their  motions  which  prevent  us  from  deducing 
conclusions  from  them  with  the  same  certainty  that  we  should  from 
those  of  solid  bodies  like  the  planets.  One  of  the  chief  difficulties  in 
investigating  the  orbits  of  comets  with  all  rigor  is  due  to  the  difficulty 
of  obtaining  accurate  positions  of  the  centre  of  so  ill-defined  an  object 
as  the  nucleus. 


PART  III 
THE   UNIVERSE  AT  LARGE. 


CHAPTER  XXII. 
INTRODUCTION. 

41,  Although  the  solar  system  comprises  the  bodies 
which  are  most  important  to  us  who  live  on  the  Earth,  yet 
they  form  only  an  insignificant  part  of  creation.  Besides 
the  Earth,  only  seven  of  the  bodies  of  the  solar  system  are 
plainly  visible  to  the  naked  eye,  whereas  some  2000  or 
more  stars  can  be  seen  on  any  clear  night.  Our  Sun  is 
simply  one  of  these  stars,  and  does  not,  so  far  as  we  know, 
differ  from  its  fellows  in  any  essential  characteristic.  It  is 
rather  less  bright  than  the  average  of  the  nearer  stars,  and 
overpowers  them  by  its  brilliancy  only  because  it  is  so  much 
nearer  to  us. 

The  distance  of  the  stars  from  each  other,  and  therefore 
from  the  Sun,  is  immensely  greater  than  any  of  the  dis- 
tances in  the  solar  system.  In  fact,  the  nearest  known  star 
is  about  seven  thousand  times  as  far  from  us  as  the  planet 
Neptune.  If  we  suppose  the  orbit  of  this  planet  to  be 
represented  by  a  child's  hoop,  the  nearest  star  would  be 
three  or  four  miles  away.  We  have  no  reason  to  suppose 
that  contiguous  stars  are,  on  the  average,  any  nearer 
together  than  this,  except  in  special  cases  where  they  are 
collected  together  in  clusters. 

369 


370  ASTRONOMY. 

The  total  number  of  the  stars  is  estimated  by  millions, 
and  they  are  separated  one  from  another  by  these  wide 
intervals.  It  follows  that,  in  going  from  the  Sun  to  the 
nearest  star,  we  are  simply  taking  a  single  step  in  the 
universe.  The  most  distant  stars  are  probably  a  thousand 
times  more  distant  than  the  nearest  one,  and  we  do  not 
know  what  may  lie  beyond  the  distant  stars. 

The  planets,  though  millions  of  miles  away,  are  compara- 
tively near  us,  and  form  a  little  family  by  themselves. 
The  planets  are,  so  far  as  we  can  see,  worlds  not  exceed- 
ingly different  from  the  Earth  on  which  we  live,  while 
the  stars  are  suns,  generally  larger  and  brighter  than  our 
own  Sun.  Each  star  may,  for  aught  we  know,  have 
planets  revolving  around  it,  but  their  distance  is  so  im- 
mense that  even  the  largest  planets  will  forever  remain  in- 
visible with  the  most  powerful  telescopes  man  can  construct. 

We  shall  see  in  what  follows  that  only  a  few  stars  are  so 
near  to  us  that  their  light  can  reach  the  Earth  in  10,  20, 
or  even  50  years.  The  vast  majority  are  so  distant  that 
the  light  which  we  now  see  left  them  a  century  ago,  or 
more.  If  one  of  these  were  suddenly  destroyed  it  would 
continue  to  shine  for  years  afterwards.  The  aspect  of 
the  sky  at  any  moment  does  not  then  represent  the  present 
state  of  the  stellar  universe,  but  rather  its  past  history. 
The  Sun's  light  is  already  eight  minutes  old.  when  it 
reaches  us;  that  of  Neptune  left  the  planet  about  four 
hours  before;  the  nearest  fixed  stars  appear  as  they  were 
no  less  than  four  years  ago  ;  while  the  Milky  Way  shines 
with  a  light  which  may  have  been  centuries  on  its  journey. 

The  difference  between  the  Earth  and  the  Sun  is  almost 
entirely  due  to  a  difference  in  their  temperature.  Nearly 
every  element  in  the  Earth  is  present  in  the  Sun.  If  the 
Earth  were  to  be  suddenly  raised  to  the  Sun's  temperature 
it  would  become  a  miniature  Sun ;  that  is,  a  miniature  star. 
Some  of  the  elements  present  in  the  Sun  are  found  to  be 


INTRODUCTION.  371 

plentiful  in  other  stars,  in  nebulae,  and  even  in  comets  and 
meteors.  All  the  bodies  of  the  solar  system  appear  to  be, 
in  the  main,  of  like  constitution;  and  their  wonderfully 
different  physical  conditions  to  be  due,  in  the  main,  to 
differences  of  temperature.  The  stars,  likewise,  are  made 
up  of  elements  often  the  same  as  the  elements  we  know  on 
the  Earth.  The  extraordinary  diversity  exhibited  by  the 
bodies  of  the  visible  universe  thus  appears  to  be  largely  due 
to  differences  in  their  temperature.  The  past  and  the 
future  of  the  Sun,  the  Earth,  and  the  Moon  can,  therefore, 
be  investigated  by  inquiring  what  temperatures  these  bodies 
have  had  in  past  times  and  what  temperatures  they  are 
likely  to  have  in  the  future. 

General  Aspect  of  the  Heavens, — Constellations. — When 
we  view  the  heavens  with  the  unassisted  eye,  the  stars 
appear  to  be  scattered  nearly  at  random  over  the  surface  of 
the  celestial  vault.  The  only  deviation  from  an  entirely 
random  distribution  which  can  be  noticed  is  a  certain 
apparent  grouping  of  the  brighter  ones  into  constellations. 
A  few  stars  are  comparatively  much  brighter  than  the  rest, 
and  there  is  every  gradation  of  brilliancy,  from  that  of 
the  brightest  to  those  which  are  barely  visible.  We  also 
notice  at  a  glance  that  the  fainter  stars  far  outnumber  the 
bright  ones;  so  that  if  we  divide  the  stars  into  classes 
according  to  their  brilliancy,  the  fainter  classes  will  contain 
the  most  stars. 

There  are  in  the  whole  celestial  sphere  about  6000  stars 
visible  to  the  naked  eye.  Of  these,  however,  we  can  never 
see  more  than  a  part  at  any  one  time,  because  one  half  of 
the  sphere  is  always  below  the  horizon.  If  we  could  see  a 
star  in  the  horizon  as  easily  as  in  the  zenith,  one  half  of  the 
whole  number,  or  3000,  would  be  visible  on  any  clear 
night.  But  stars  near  the  horizon  are  seen  through  so 
great  a  thickness  of  atmosphere  as  greatly  to  obscure  their 
light;  consequently  only  the  brightest  ones  can  there  be 


372  ASTRONOMY. 

seen.  It  is  not  likely  that  more  than  2000  stars  can  ever 
be  taken  in  at  a  single  view  by  any  ordinary  eye.  About 
2000  other  stars  are  so  near  the  south  pole  that  they  never 
rise  in  our  latitudes.  Hence  ont  of  the  6000  visible,  only 
4000  ever  come  within  the  range  of  our  vision,  unless  we 
make  a  journey  toward  the  equator. 

The  Galaxy. — The  Galaxy,  or  Milky  Way,  is  a  magnifi- 
cent stream  or  belt  of  white  milky  light  10°  or  15°  in 
breadth,  extending  obliquely  around  the  celestial  sphere. 
During  the  spring  months  it  nearly  coincides  with  our 
horizon  in  the  early  evening,  but  it  can  be  seen  at  all  other 
times  of  the  year  spanning  the  heavens  like  an  arch.  For 
a  portion  of  its  length  it  is  split  longitudinally  into  two 
parts,  which  remain  separate  through  many  degrees,  and 
are  finally  united  again.  The  student  will  obtain  a  better 
idea  of  it  by  actual  examination  than  from  any  description. 
He  will  see  that  its  irregularities  of  form  and  lustre  are 
such  that  in  some  places  it  looks  like  a  mass  of  brilliant 
clouds  (see  Fig.  199). 

When  GALILEO  first  directed  his  telescope  to  the  heavens, 
about  the  year  1610,  he  perceived  that  the  Milky  Way  was 
composed  of  stars  too  faint  to  be  individually  seen  by  the 
unaided  eye.  HUYGHENS  in  1656  resolved  a  large  portion 
of  the  Galaxy  into  stars,  and  concluded  that  it  was  com- 
posed entirely  of  them.  KEPLER  considered  it  to  be  a  vast 
ring  of  stars  surrounding  the  solar  system,  and  remarked 
that  the  Sun  must  be  situated  near  the  centre  of  the  ring. 
This  view  agrees  very  well  with  the  one  now  received, 
except  that  the  stars  which  form  the  Milky  Way,  instead 
of  lying  near  to  the  solar  system,  as  KEPLER  supposed,  are 
at  distances  so  vast  as  to  elude  all  our  powers  of  imagina- 
tion. 

The  most  recent  researches  have  shown  that  the  Milky 
Way  is  a  vast  cluster  of  stars  intermixed  with  nebulae,  and 
that  these  stars  and  nebulae  are,  in  all  probability,  physi- 


INTRODUCTION. 


373 


374:  ASTRONOMY. 

cally  connected  and  not  merely  perspectively  projected  in 
the  same  part  of  the  sky.  A  majority  of  its  stars  are  of  the 
same  spectral  type  (like  Sirius).  Nearly  all  the  gaseous 
nebnlae  are  in  this  region;  and  most  of  the  stars  with 
bright-line  spectra  are  here.  We  must  then  consider  the 
Milky  Way  as  mainly  a  physical  system,  and  only  partly  as 
a  geometrical  appearance. 

Lucid  and  Telescopic  Stars. — When  we  view  the  heavens  with  a 
telescope,  we  find  that  there  are  innumerable  stars  too  small  to  be 
seen  by  the  naked  eye.  We  may  therefore  divide  the  stars,  with  re- 
spect to  brightness,  into  two  great  classes. 

Lucid  Stars  are  those  which  are  visible  without  a  telescope. 

Telescopic  Stars  are  those  which  are  not  so  visible. 

Magnitudes  of  the  Stars.— The  stars  were  classified  by  PTOLEMY 
into  six  orders  of  magnitude.  The  fourteen  brightest  visible  in  our 
latitudes  were  designated  as  of  the  first  magnitude,  while  those  barely 
visible  to  the  naked  eye  were  said  to  be  of  the  sixth  magnitude.  This 
classification  is  entirely  arbitrary,  since  there  are  no  two  stars  of  ab- 
solutely the  same  brightness.  If  all  the  stars  were  arranged  in  the 
order  of  their  actual  brilliancy,  we  should  find  a  regular  gradation 
from  the  brightest  to  the  faintest,  no  two  being  precisely  the  same. 
Between  the  north  pole  and  35°  south  declination  there  are  : 

14  stars  of  the  first  magnitude. 

48    "        "       second      " 
152    "         "       third 
313    "         "       fourth      " 
854    "         "       fifth 
3974    "        "       sixth 

5355  of  the  first  six  magnitudes. 

Of  these,  however,  nearly  2000  of  the  sixth  magnitude  are  so  faint 
that  they  can  be  seen  only  by  an  eye  of  extraordinary  keenness. 
Measures  of  the  light  of  the  stars  show  that  a  star  of  the  second 
magnitude  is  four  tenths  as  bright  as  one  of  the  first ;  one  of  the  third 
is  four  tenths  as  bright  as  one  of  the  second,  and  so  on.  The  ratio 
^  is  called  the  light-ratio. 

The    Constellations  and   Names  of   the    Stars.  —  The 
ancients  divided  the  stars   into  constellations,  and  gave 


INTRODUCTION.  375 

special  names  to  these  groups  and  to  many  of  the  more 
conspicuous  stars  also. 

Considerably  more  than  3000  years  before  the  commencement  of  the 
Christian  chronology  the  star  Sirius,  the  brightest  in  the  heavens,  was 
known  to  the  Egyptians  under  the  name  of  Sothis.  The  seven  stars 
of  the  Great  Bear,  so  conspicuous  in  our  northern  sky,  were  known 
under  that  name  to  HOMER  (800  B.C.),  as  well  as  the  group  of  the 
Pleiades,  or  Seven  Stars,  and  the  constellation  of  Orion.  All  the 
earlier  civilized  nations,  Egyptians,  Chinese,  Greeks,  and  Hindoos, 
had  some  arbitrary  division  of  the  surface  of  the  heavens  into  irregu- 
lar and  often  fantastic  shapes,  which  were  distinguished  by  names. 
The  area  within  which  the  Sun  and  planets  move — the  Zodiac — was 
probably  divided  and  named  before  the  year  2000  B.C.,  and  the  48 
constellations  given  by  PTOLEMY  were  probably  formed  at  least  as 
early  as  this  time. 

In  early  times  the  names  of  heroes  and  animals  were  given  to  the 
constellations.  Each  figure  was  supposed  to  be  painted  on  the  sur- 
face of  the  heavens,  and  the  stars  were  designated  by  their  position 
upon  some  portion  of  the  figure.  The  ancient  and  mediaeval  astrono- 
mers spoke  of  "the  bright  star  in  the  left  foot  of  Orion"  "the  eye 
of  the  Bull"  "the  heart  of  the  Lion"  "the  head  of  Perseus,"  etc. 
These  figures  are  still  retained  upon  some  star-charts,  and  are  useful 
where  it  is  desired  to  compare  the  older  descriptions  of  the  constella- 
tions with  our  modern  maps.  Otherwise  they  have  ceased  to  serve 
any  really  useful  purpose,  and  are  often  omitted  from  maps  designed 
for  purely  astronomical  uses. 

The  Arabians  gave  special  names  to  a  large  number  of  the  brighter 
stars.  Some  of  these  names  are  in  common  use  at  the  present  time, 
as  Aldebaran,  Fomalhaut,  etc. 

In  1654  BAYER,  of  Germany,  mapped  the  constellations  and  desig- 
nated the  brighter  stars  of  each  constellation  by  the  letters  of  the 
Greek  alphabet.  When  this  alphabet  was  exhausted  he  introduced 
the  letters  of  the  Eoman  alphabet.  In  general,  the  brightest  star 
was  designated  by  the  first  letter  of  the  alphabet,  a,  the  next  by  the 
following  letter,  ft,  etc. 

On  this  system,  a  star  is  designated  by  a  certain  Greek  letter,  fol- 
lowed by  the  genitive  of  the  Latin  name  of  the  constellation  to  which 
it  belongs.  For  example  a  Canis  Majoris,  or,  in  English,  a  of  the 
Great  Dog,  is  the  designation  of  Sirius,  the  brightest  star  in  the 
heavens.  The  brightest  stars  of  the  Great  Bear  are  called  a  Ursa 
Mujoris,  /3  Ursce  Majoris,  etc.  Arcturus  is  a  Bootis.  The  student 


376  ASTRONOMY. 

will  here  see  a  resemblance  to  our  way  of  designating  individuals  by 
a  Christian  name  followed  by  the  family  name.  The  Greek  letters 
furnish  the  Christian  names  of  the  separate  stars,  while  the  name  of 
the  constellation  is  that  of  the  family.  As  there  are  only  fifty  letters 
in  the  two  alphabets  used  by  BAYER,  only  the  fifty  brightest  stars  in 
each  constellation  could  possibly  be  designated  by  this  method. 

After  the  telescope  had  fixed  the  position  of  many  additional  stars, 
some  other  method  of  denoting  them  became  necessary.  FLAMSTEED, 
about  the  year  1700,  prepared  an  extensive  catalogue  of  stars,  in 
which  those  of  each  constellation  were  designated  by  numbers  in  the 
order  of  right-ascension.  These  numbers  were  entirely  independent 
of  the  designations  of  BAYER— that  is,  he  did  not  omit  the  BAYER 
stars  from  his  system  of  numbers,  but  numbered  them  as  if  they 
had  no  Greek  letter.  Hence  those  stars  to  which  BAYER  applied 
letters  have  two  designations,  the  number  and  the  letter.  The  fainter 
stars  are  designated  nowadays  either  by  their  R.A.  and  Decl.,  or  by 
their  numbers  in  some  well-known  catalogue  of  stars. 

Numbering  and  Cataloguing  the  Stars. — As  telescopic  power  is  in- 
creased,  we  still  find  fainter  and  fainter  stars.  But  the  number 
cannot  go  on  increasing  forever  in  the  same  ratio  as  the  brighter 
magnitudes,  because,  if  it  did,  the  whole  night  sky  would  be  a  blaze 
of  starlight,  instead  of  a  dark  sphere  dotted  with  brilliant  points. 

If  telescopes  with  powers  far  exceeding  our  present  ones  are  made, 
they  will,  no  doubt,  show  very  many  new  stars.  But  it  is  highly 
probable  that  the  number  of  such  successive  orders  of  stars  would 
not  increase  in  the  same  ratio  as  is  observed  in  the  8th,  9th,  and  10th 
magnitudes,  for  example. 

In  special  regions  of  the  sky,  which  have  been  searchingly  ex- 
amined by  various  telescopes  of  successively  increasing  apertures, 
the  number  of  new  stars  found  is  by  no  means  in  proportion  to  the 
increased  instrumental  power.  If  this  is  found  to  be  true  elsewhere, 
the  conclusion  may  be  that,  after  all,  the  stellar  system  can  be  ex- 
perimentally shown  to  be  of  finite  extent,  or  to  contain  only  a  finite 
number  of  stars,  rather. 

We  have  already  stated  that  in  the  whole  sky  an  eye  of  average 
power  will  see  about  6000  stars.  With  a  telescope  this  number  is 
greatly  increased,  and  the  most  powerful  telescopes  of  modern  times 
will  probably  show  more  than  100,000,000  stars. 

In  ARQELANDER'S  Durchmusterung  of  the  stars  of  the  northern 
heavens  there  are  recorded  as  belonging  to  the  northern  hemisphere 
314,926  stars  from  the  first  to  the  9.5  magnitude,  so  that  there  are 
about  600,000  in  the  whole  heavens. 


INTRODUCTION. 


377 


We  can  readily  compute  the  amount  of  light  received  by  the  Earth 
on  a  clear  but  moonless  night  from  these  stars.  The  brightness  of 
an  average  star  of  the  first  magnitude  is  0.5  of  that  of  a  Lyrce.  A 
star  of  the  2d  magnitude  will  shine  with  a  light  expressed  by 
0.5  X  0.4  =  0.20,  and  so  on.  (See  p.  374.) 


The  total  brightness  of 


10 

1st  magnitude  stars  is    5.6] 

37 

2d 

7.4  | 

128 

3d 

102  ! 

310 

4th 

9.9  f 

1,016 

5th 

13.0  | 

4,328 

6th 

22  1J 

13,593 

7th 

27  8  ) 

57,960 

8th 

47.4  f 

Sum  =  142.8 

It  thus  appears  that  from  the  stars  to  the  8th  magnitude,  inclusive, 
we  receive  143  times  as  much  light  as  from  a  Lyrce.  a  Lyrce  -has 
been  determined  by  ZOLLNER  to  be  about  44, 000, 000, 000  times  fainter 
than  the  Sun,  so  that  the  proportion  of  starlight  to  sunlight  can  be 
computed.  It  also  appears  that  the  stars  too  faint  to  be  individually 
visible  to  the  naked  eye  are  yet  so  numerous  as  to  affect  the  general 
brightness  of  the  sky  more  than  the  so-called  lucid  stars  (1st  to  6th 
magnitude).  The  sum  of  the  last  two  numbers  of  the  table  is  greater 
than  the  sum  of  all  the  others. 

The  Star  Maps  printed  in  this  book  furnish  a  means 
by  which  the  constellations  and  principal  stars  can  be 
identified  by  the  student. 

Maps  of  the  stars  down  to  the  14th  or  15th  magnitude 
are  now  made  by  photography,  using  special  telescopes  and 
long  exposures  (two  or  three  hours).  Such  complete  maps 
as  this  will  throw  a  flood  of  light  on  the  distribution  arid 
arrangement  of  the  constituent  stars  of  the  Stellar  Uni- 
verse. 

The  Stars  are  Suns. — Spectroscopic  observations  prove 
that  nearly  all  of  the  stars  are  suns,  very  like  our  own 
Sun.  They  are  self-luminous  and  intensely  hot.  They 
have  extensive  atmospheres  of  incandescent  gases  and 
metallic  vapors.  The  light  from  a  whole  class  of  stars  is, 


378  ASTRONOMY. 

so  far  as  can  be  determined,  precisely  like   sunlight  in 
quality.     We  may  say  in  general  that  stars  are  suns. 

The  light  received  from  even  the  brightest  star  is  a  very  small 
quantity  because  even  the  nearest  star  is  very  distant.     From  Sirius, 

the  brightest  star  in  the  sky,  we  receive  of  the  light 


received  from  the  Sun.  Let  I  be  the  light  received  from  a  star 
at  a  distance  D  from  us  and  L  the  light  we  should  receive  from  this 
star  if  it  were  at  the  Sun's  distance  from  us  (=  1).  Then 

L  :  I  =  1  :  -^j-  or  L  =  I  .  D*. 

In  the  case  of  Sirius,  I  =  as  above,  and  D  =  about 

542,000  times  the  Sun's  distance.     Hence  L  =  * 


7  0000000  ' 

That  is,  Sirius  emits  forty-two  times  as  much  light  (and  presumably 
about  forty-two  times  as  much  heat)  as  the  Sun.  The  Sun  is  a 
small  star,  compared  to  Sirius.  The  pole-star,  Polaris,  emits  about 
two  hundred  times  as  much  light  as  the  Sun,  while  the  light  received 
from  it  is  insignificant  compared  to  sunlight. 

If  we  compare  stars  with  the  Sun  in  this  way  we  shall 
see  that  some  of  them  emit  several  thousand  times  more 
light,  while  some  emit  perhaps  -3-5*5-5-  Par*i  as  much  light. 
These  are  great  differences,  but  they  are  not  enormous. 

The  masses  of  a  few  stars  are  known.  It  is  found  that 
some  of  these  stars  have  masses  perhaps  a  hundred  times 
greater,  while  others  have  masses  very  much  smaller,  than 
the  Sun's  mass.  Here  again  there  are  great  differences, 
but  the  differences  are  not  enormous.  Our  Sun  is  an 
average  star,  we  may  say. 


CHAPTER   XXIII. 
MOTIONS  AND  DISTANCES  OF  THE   STARS. 

42.  Proper  Motions. — To  the  unaided  vision,  the  fixed 
stars  appear  to  preserve  the  same  relative  position  in  the 
heavens  through  many  centuries,  so  that  if  the  ancient 
astronomers  could  again  see  them,  they  could  detect  only 
the  slight  changes  in  their  arrangement.  But  the  accurate 
measurements  of  modern  times  show  that  there  are  slow 
changes  in  the  positions  of  the  brighter  stars.  Many  of 
them  have  small  motions  on  the  celestial  sphere.  Their 
right-ascensions  and  declinations  change  (slightly)  from 
year  to  year,  apparently  with  uniform  velocity.  The 
changes  are  called  proper  motions,  since  they  are  real 
motions  peculiar  to  the  star  itself. 

In  general,  the  proper  motions  even  of  the  brightest  stars 
are  only  a  fraction  of  a  second  of  arc  in  a  year,  so  that 
thousands  of  years  would  be  required  for  them  to  change 
their  place  in  any  striking  degree,  and  hundreds  of  thou- 
sands to  make  a  complete  revolution  around  the  celestial 
sphere.  The  circumference  of  a  sphere  contains  1,296,000". 

Proper  Motion  of  the  Sun. — It  is  a  priori  evident  that 
stars,  in  general,  must  have  proper  motions,  when  once  we 
admit  the  universality  of  gravitation.  That  any  fixed  star 
should  be  entirely  at  rest  would  require  that  the  attractions 
on  all  sides  of  it  should  be  exactly  balanced.  Any — the 
slightest — change  in  the  position  of  this  star  would  break 
up  this  balance,  and  thus,  in  general,  it  follows  that  stars 
must  be  in  motion,  since  each  of  them  cannot  occupy  such 
a  critical  position  as  has  to  be  assumed. 

379 


380  ASTRONOMY. 

If  but  one  fixed  star  is  in  motion,  all  the  rest  are  affected, 
and  we  cannot  donbt  that  every  single  star,  our  Sun  in- 
cluded, is  in  motion  by  amounts  which  vary  from  small  to 
great.  If  the  Sun  alone  has  a  motion,  and  all  the  other 
stars  are  at  rest,  the  consequence  would  be  that  all  the  fixed 
stars  would  appear  to  be  retreating  en  masse  from  that 
point  in  the  sky  toward  which  we  were  moving.  Those 
nearest  us  would  move  more  rapidly,  those  more  distant 
less  so.  And  in  the  same  way,  the  stars  from  which  the 
solar  system  was  receding  would  seem  to  be  approaching 
each  other. 

If  the  stars,  instead  of  being  quite  at  rest,  as  just  sup- 
posed, have  motions  proper  to  themselves,  as  they  do,  then 
we  shall  have  a  double  complexity.  They  would  still 
appear  to  an  observer  in  the  solar  system  to  have  motions. 
One  part  of  these  motions  would  be  truly  proper  to  the 
stars,  and  one  part  would  be  due  to  the  advance  of  the 
Sun  itself  in  space. 

Observations  of  the  positions  of  stars — of  their  right- 
ascensions  and  declinations — can  show  only  the  resultant 
of  these  two  motions.  It  is  for  reasoning  to  separate  this 
resultant  into  its  two  components.  The  first  question  is  to 
determine  whether  the  results  of  observation  indicate  any 
solar  motion  at  all.  If  there  is  none,  the  proper  motions 
of  stars  will  be  directed  along  all  possible  lines.  If  the  Sun 
does  truly  move  in  space  along  some  line,  then  there  will 
be  a  general  agreement  in  the  resultant  motions  of  the  stars 
near  the  ends  of  the  line  along  which  it  moves,  while  those 
at  the  sides,  so  to  speak,  will  show  comparatively  less  sys- 
tematic effect.  It  is  as  if  one  were  riding  in  the  rear  of  a 
railway  train  and  watching  the  rails  over  which  it  has  just 
passed.  As  we  recede  from  any  point,  the  rails  at  that 
point  seem  to  come  nearer  and  nearer  together. 

If  we  were  passing  through  a  forest,  we  should  see  the 
trunks  of  the  trees  from  which  we  were  going  apparently 


MOTIONS  AND  DISTANCES  OF  THE  STARS.      381 

come  nearer  and  nearer  together,  while  those  on  the  sides 
of  us  would  remain  at  their  constant  distance,  and  those  in 
front  would  grow  further  and  further  apart. 

These  phenomena,  that  occur  in  a  case  where  we  are 
sensible  of  our  own  motion,  serve  to  show  how  we  may  de- 
duce a  motion,  otherwise  unknown,  from  the  appearances 
which  are  presented  by  the  stars  in  space. 

In  this  way,  acting  upon  suggestions  which  had  been 
thrown  out  previously  to  his  own  time,  Sir  WILLIAM 
HERSCHEL  demonstrated  that  the  Sun,  together  with  all  its 
system,  was  moving  through  space  in  an  unknown  and 
majestic  orbit  of  its  own.  The  centre  round  which  this 
motion  is  directed  cannot  yet  be  assigned.  We  can  only 
determine  the  point  in  the  heavens  toward  which  our 
course  is  directed — "  the  apex  of  solar  motion." 

A  number  of  astronomers  have  since  investigated  this 
motion  with  a  view  of  determining  the  exact  point  in  the 
heavens  toward  which  the  Sun  is  moving.  Their  results 
differ  slightly,  but  the  points  toward  which  the  Sun  is 
moving  all  fall  in  or  near  the  constellation  Hercules  not  far 
from  the  bright  star  Alpha  Lyrce  (Yega).  The  amount  of 
the  motion  is  such  that  if  the  Sun  were  viewed  at  right 
angles  to  the  direction  of  motion  from  an  average  star  of 
the  first  magnitude,  it  would  appear  to  move  about  one 
third  of  a  second  per  year. 

Spectroscopic  observations  will  give  the  direction  and  the 
amount  of  the  solar  motion  in  another  and  an  independent 
way  (see  Chapter  XVII). 

Distances  of  the  Fixed  Stars. — The  ancient  astronomers 
supposed  all  the  fixed  stars  to  be  situated  at  a  short  distance 
outside  of  the  orbit  of  the  planet  Saturn,  then  the  outer- 
most known  planet.  The  idea  was  prevalent  that  Nature 
would  not  waste  space  by  leaving  a  great  region  beyond 
Saturn  entirely  empty. 

When  COPERNICUS  announced  the  theory  that  the  Sun 


382  ASTRONOMY. 

was  at  rest  and  the  Earth  in  motion  around  it,  the  problem 
of  the  distance  of  the  stars  acquired  a  new  interest.  It 
was  evident  that  if  the  Earth  described  an  annual  orbit, 
then  the  stars  would  appear  in  the  course  of  a  year  to  oscil- 
late back  and  forth  in  corresponding  orbits,  unless  they 
were  so  immensely  distant  that  these  oscillations  were  too 
small  to  be  seen. 

The  apparent  oscillation  of  Mars  produced  in  this  way 
was  described  p.  188  et  seq.  These  oscillations  were,  in 
fact,  those  which  the  ancients  represented  by  the  motion 
of  the  planet  around  a  small  epicycle  (see  Fig.  124).  But 


FIG.  200.— THE  THEORY  OF  PARALLAX. 

no  such  oscillation  was  detected  in  a  fixed  star  until  the 
year  1837;  and  this  fact  seemed  to  the  astronomers  of 
GALILEO'S  time  to  present  an  almost  insuperable  difficulty 
in  the  reception  of  the  Copernican  system.  As  the  instru- 
ments of  observation  were  from  time  to  time  improved,  this 
apparent  annual  oscillation  of  the  stars  was  ardently  sought 
for. 

The  parallax  of  a  planet  (P  in  the  figure)  is  the  angle  at 
the  planet  subtended  by  the  Earth's  radius  (OS'  =  4000 
miles).  The  annual  parallax  of  a  star  (P)  is  the  angle  at 


MOTIONS  AND  DISTANCES  OF  THE  STARS.       383 

the  star  subtended  by  the  radius  of  the  Earth's  orbit 
(CS1  =  93,000,000  miles).  See  page  109.  The  annual 
parallax  of  Saturn  is  about  6°  and  of  Neptune  it  is  about 
2°,  and  these  are  angles  easily  detected  with  the  astronomi- 
cal instruments  of  the  ancients.  It  was  very  evident,  with- 
ont  telescopic  observation,  that  the  stars  could  not  have  a 
parallax  of  one  half  a  degree.  A  change  of  place  of  one 
half  a  degree  could  be  readily  detected  by  the  naked  eye. 
They  must  therefore  be  at  least  twelve  times  as  far  as 
Saturn  if  the  Copernican  system  were  true. 

When  the  telescope  was  applied  to  measurement,  a  con- 
tinually increasing  accuracy  was  gained  by  the  improve- 
ment of  the  instruments.  Yet  the  parallax  of  the  fixed 
stars  eluded  measurement.  Early  in  the  present  century 
it  became  certain  that  even  the  brighter  stars  had  not,  in 
general,  an  annual  parallax  so  great  as  1",  and  thus  it 
became  certain  that  they  must  lie  at  a  greater  distance  than 
200,000  times  that  which  separates  the  Earth  from  the  Sun 
(see  page  23).  R  -  206,264". 

Success  in  actually  measuring  the  parallax  of  the  stars 
was  at  length  obtained  almost  simultaneously  by  two 
astronomers,  BESSEL  of  Konigsberg  and  STRUVE  of  Dorpat. 
BESSEL  selected  61  Cygni  for  observation,  in  August,  1837. 
The  result  of  two  or  three  years  of  observation  was  that 
this  star  had  a  parallax  of  about  one  third  of  a  second. 
This  would  make  its  distance  from  the  Sun  nearly  600,000 
astronomical  units.  The  reality  of  this  parallax  has  been 
well  established  by  subsequent  investigators,  only  it  has 
been  shown  to  be  a  little  larger,  and  therefore  the  star  a 
little  nearer  than  BESSEL  supposed.  The  most  probable 
parallax  is  now  found  to  be  0".45,  corresponding  to  a  dis- 
tance of  about  400,000  radii  of  the  Earth's  orbit. 

The  distances  of  the  stars  are  frequently  expressed  by  the 
time  required  for  light  to  pass  from  them  to  our  system. 
The  velocity  of  light  is,  it  will  be  remembered,  about 


384 


ASTRONOMY. 


300,000  kilometres  per  second,  or  such  as  to  pass  from  the 
Sun  to  the  Earth  in  8  minutes  18  seconds. 

The  cut  shows  the  arrangement  of  some  of  the  nearer 
stars  in  space.  They  are  shown  on  a  plane,  and  not  in 
solid  space.  The  dot  in  the  centre  of  the  figure  is  the 
solar  system.  The  circles  of  the  figure  stand  for  spheres, 


FIG  201. 


whose  radii  are  5,  10,  15,  20,  25,  30  light-years;  that  is, 
for  spheres  whose  radii  are  of  such  lengths  that  light, 
which  moves  186,000  miles  in  a  second  requires  5,  10,  etc., 
years  to  traverse  these  radii. 

The  time  required  for  light  to  reach  the  Earth  from  a 


MOTIONS  AND  DISTANCES  OF  THE  STARS.      385 


few  of  the  stars,  whose  parallax  has  been  measured,  is  as 
follows : 


STAR. 

Years. 

STAR. 

Years. 

4£ 

Vega  (aLyrae)  

27 

7 

AldebaTan  (at  Tauri)  

32 

Sirius  (a  Canis  majoris).  .  .  . 
Procyon  (a:  Canis  minoris)  .. 

8 
12 

Polaris  (a  Ursae  minoris). 
Arcturus  (aBoOtis)  ... 

47 
160 

If  the  star  Polaris  were  to  be  suddenly  destroyed — now 
— this  instant — its  light  would  continue  to  shine  for  nearly 
half  a  century  more. 


CHAPTER  XXIV. 

VARIABLE  AND   TEMPORARY   STARS. 

43.  Stars  Regularly  Variable. — Since  the  end  of  the 
sixteenth  century,  it  has  been  known  that  all  stars  do  not 
shine  with  a  constant  light.  The  period  of  a  variable  star 
is  the  interval  of  time  daring  which  it  goes  through  all  its 
changes,  and  returns  to  its  original  brilliancy. 

The  most  noted  variable  stars  are  Mira  Ceti  (o  Ceti) 
(star-map  VI,  in  the  southeast)  and  Algol  (/3  Persei)  (star- 
map  I,  near  the  zenith).  Mira  is  usually  a  ninth-magni- 
tude star  and  is  therefore  invisible  to  the  naked  eye. 
Erery  eleven  months  it  increases  to  its  greatest  brightness 
(sometimes  as  high  as  the  2d  magnitude,,  sometimes  not 
above  the  4th),  remaining  at  this  maximum  for  some  time, 
then  gradually  decreases  until  it  again  becomes  invisible  to 
the  naked  eye,  and  so  remains  for  about  five  or  six  months. 
The  average  period,  from  minimum  to  minimum,  is  about 
333  days,  but  the  period  varies  greatly.  It  has  been  known 
as  a  variable  since  1596. 

Algol  has  been  known  as  a  variable  star  since  1667. 
This  star  is  commonly  of  the  2d  magnitude;  after  remain- 
ing so  about  2|  days,  it  falls  to  4th  magnitude  in  the  short 
time  of  4-J  hours,  and  remains  of  4th  magnitude  for  20 
minutes.  It  then  increases  in  brilliancy,  and  in  another 
3£  hours  it  is  again  of  the  2d  magnitude,  at  which  point  it 
remains  for  the  rest  of  its  period,  about  2d  12h. 

These  examples  of  two  classes  of  variable  stars  give  an 
idea  of  the  extraordinary  nature  of  the  phenomena  they 
present. 

386 


VARIABLE  AND   TEMPORARY  STARS.  387 

Several  hundred  stars  are  known  to  be  variable.  A  short 
list  of  variables  is  given  in  Table  VII. 

The  color  of  more  than  three  fourths  of  the  variable  stars 
is  red  or  orange.  It  is  a  very  remarkable  fact  that  certain 
star-clusters  contain  large  numbers  of  variable  stars. 

Temporary  or  "New"  Stars. — There  are  a  few  cases 
known  of  stars  that  have  suddenly  appeared,  attained  more 
or  less  brightness,  and  slowly  decreased  in  magnitude, 
either  disappearing  totally,  or  finally  remaining  as  compara- 
tively faint  objects.  A  new  star  that  appeared  in  134  B.C. 
led  HIPPARCHUS  to  form  his  catalogue  of  stars. 

The  most  famous  new  star  appeared  in  1572,  and  attained 
a  brightness  greater  than  that  of  Jupiter.  It  was  even 
visible  to  the  eye  in  daylight.  TYCHO  BRAHE  first  observed 
this  star  in  November,  1572,  and  watched  its  gradual 
increase  in  light  until  its  maximum  in  December.  It  then 
began  to  diminish  in  brightness,  and  in  January,  1573,  it 
was  fainter  than  Jupiter.  In  February  it  was  of  the  1st 
magnitude,  in  April  of  the  2d,  in  July  of  the  3d,  and  in 
October  of  the  4th.  It  continued  to  diminish  until  March, 
1574,  when  it  became  invisible  to  the  naked  eye. 

The  history  of  temporary  stars  is,  in  general,  similar  to 
that  of  the  star  of  1572,  except  that  none  have  attained  so 
great  a  degree  of  brilliancy.  As  more  than  a  score  of  such 
objects  are  known  to  have  appeared,  many  of  them  before 
the  making  of  accurate  observations,  it  is  probable  that 
many  others  have  appeared  without  recognition.  Among 
telescopic  stars  there  is  but  a  small  chance  of  detecting  a 
new  or  temporary  star. 

Theories  to  Account  for  Variable  Stars. — Two  main 
classes  of  variable  stars  exist  and  two  theories  must  be 
mentioned  here. 

I.  Stars  in  general,  like  the  Sun,  are  subject  to  erup- 
tions of  glowing  gas  from  their  interior,  and  to  the  forma- 
tion of  dark  spots  on  their  surfaces.  These  eruptions  and 


388  ASTRONOMY. 

formations  have  in  most  cases  a  greater  or  less  tendency  to 
a  regular  period,  like  the  period  of  a  gigantic  geyser. 

In  the  case  of  our  San,  the  period  is  11  years,  but  in  the 
case  of  many  of  the  stars  it  is  much  shorter.  Ordinarily, 
as  in  the  case  of  the  Sun  and  of  a  large  majority  of  the 
stars,  the  variations  are  too  slight  to  affect  the  total  quan- 
tity of  light  to  any  noteworthy  extent. 

In  the  case  of  the  variable  stars  this  spot-producing 
power  and  the  liability  to  eruptions  are  very  much  greater, 
and  we  have  changes  of  light  sufficiently  marked  to  be  per- 
ceived by  the  eye. 

This  theory  explains  why  so  large  a  proportion  of  the 
variable  stars  are  red.  It  is  well  known  that  glowing 
bodies  emit  a  larger  proportion  of  red  rays,  and  a  smaller 
proportion  of  blue  ones,  the  cooler  they  become.  It  is 
therefore  probable  that  the  red  stars  have  the  least  heat. 
This  being  the  case,  spots  are  more  easily  produced  on 
their  surfaces  just  as  cooling  iron  is  covered  with  a  crust. 
If  their  outside  surface  is  .so  cool  as  to  become  solid  in 
certain  regions,  the  glowing  gases  from  the  interior  will 
burst  through  with  more  violence  than  if  the  surrounding 
shell  were  liquid  or  gaseous.  The  cause  of  the  periodic 
nature  of  these  eruptions  is  probably  similar  to  the  cause 
of  the  periodic  outbursts  of  geysers. 

II.  There  is,  however,  another  class  of  variable  stars 
whose  variations  are  due  to  an  entirely  different  cause; 
Algol  is  the  best  representative  of  the  class.  The  extreme 
regularity  with  which  the  light  of  this  object  fades  away 
and  disappears  suggests  the  possibility  that  a  dark  body 
may  be  revolving  around  it,  partially  eclipsing  it  at  every 
revolution.  The  law  of  variation  of  its  light  is  so  different 
from  that  of  the  light  of  most  other  variable  stars  as  to  sug- 
gest a  different  cause.  Most  others  are  near  their  maximum 
for  only  a  small  part  of  their  period,  while  Algol  is  at  its 
maximum  for  nine  tenths  of  it.  Others  are  subject  to 


VARIABLE  AND  TEMPORARY  STARS.  389 

nearly  continuous  changes,  while  the  light  of  Algol  remains 
constant  during  nine  tenths  of  its  period.  Spectroscopic 
observations  show  that  Algol  (a  bright  body)  is  accompanied 
by  a  dark  satellite  that  revolves  about  it  in  an  orbit  which 
is  presented  to  us  nearly  edgewise.  The  satellite  is  about 
as  large  in  diameter  as  Algol  and  is  about  3,000,000  miles 
distant  from  it.  When  the  dark  satellite  is  in  front  of 
Algol  some  of  its  light  is  cut  off.  When  it  is  to  one  side, 
Algol  shines  with  its  full  brightness,  and  we  do  not  see  the 
satellite  because  it  is  not  self-luminous.  Probably  both 
Algol  and  its  dark  companion  revolve  about  a  third  dark 
star.  The  diameter  of  Algol  is  about  1,000,000  miles.  The 
diameter  of  the  dark  satellite  is  about  800,000  miles. 
Each  of  these  stars  is  about  the  size  of  our  Sun.  The 
mass  of  both  combined  is  about  f  of  the  Sun's  mass. 
Their  density  is  therefore  much  less  than  that  of  water. 
They  are  like  heavy  spherical  clouds. 

Dark  Stars. — The  existence  of  "  dark  stars  "  is  proved  in  several 
ways.  Algol  and  other  stars  of  its  class  are  accompanied  by  non- 
luminous  satellites,  as  is  shown  by  the  phenomena  of  their  variability. 
8m us  and  Procyon  are  also  so  accompanied,  as  is  demonstrated  by 
periodic  irregularities  of  their  motion.  There  is  no  reason  why 
there  may  not  be  "as  many  dark  stars  as  bright  ones."  A  bright 
star  is  one  that  is  (comparatively)  young.  Its  heat  is  still  so  ardent 
as  to  make  it  self-luminous.  A  dark  star  is  one  that  has  lost  its  heat 
in  the  lapse  of  centuries— probably  thousands  of  centuries.  In  our 
own  solar  system  Jupiter  was  probably  a  self-luminous  planet  not  so 
very  many  centuries  ago.  The  Earth  and  other  planets  are  dark, 
but  still  have  some  of  their  native  heat.  The  moon  is  dark  (i.  e.,  not 
self-luminous)  and  it  is  also  cold. 

We  must  figure  the  stellar  universe  to  ourselves  as  containing  not 
only  the  stars  that  we  see,  but  also  as  containing  perhaps  as  many 
more  that  we  shall  never  see,  because  they  have  lost  the  light  and 
heat  that  they  (probably)  once  possessed.  Most  of  the  dark  stars  will 
forever  remain  unknown  to  us,  but  occasionally  we  meet  with  cases 
like  those  of  Algol  or  of  Sirius,  which  make  it  certain  that  dark 
stars  exist.  Their  is  reason  to  believe  that  their  number  is  very 
large. 


CHAPTER  XXV. 

DOUBLE,    MULTIPLE,    AND  BINARY   STARS. 

44.  Double  and  Multiple  Stars. — When  we  examine  the 
heavens  with  telescopes,  we  find  many  cases  in  which  two 
or  more  stars  are  extremely  close  together,  so  as  to  form  a 
pair,  a  triplet,  or  a  group.  It  is  evident  that  there  are  two 
ways  to  account  for  this  appearance. 

1.  We  may  suppose  that  the  stars  happen  to  lie  nearly 
in  the  same  straight  line  from  the  Earth,  but  have  no  con- 
nection with  each  other.     It  is  evident  that  in  this  case 
a  pair  of  stars  might   appear   doable,   although  one  was 
hundreds  or  thousands  of  times  farther  off  than  the  other. 
It  is,  moreover,  impossible,  from  mere  inspection,  to  deter- 
mine which  is  the  farther  off.     (See  Fig.  3,  ^,  £,  t). 

2.  We    may   suppose   that    the    stars   are   really   near 
together,  as  they  appear,  and  do,  in  fact,  form  a  connected 
pair  or  group. 

A  couple  of  stars  in  the  first  case  is  said  to  be  optically 
double. 

Stars  that  are  really  physically  connected  are  said  to  be 
physically  double.  Their  physical  connection  can  only  be 
proved  by  observations  which  show  that  the  two  stars  are 
revolving  about  their  common  centre  of  gravity.  There 
are  tens  of  thousands  of  stars  in  the  sky  that  appear  to  be 
double  and  hundreds  that  have  already  been  proved  to  be 
physically  connected. 

There  are  several  cases  of  stars  which  appear  double  to  the  naked 
eye.  e  Lyra  is  such  a  star  and  is  an  interesting  object  in  a  small 
telescope,  from  the  fact  that  each  of  the  two  stars  which  compose  it 

390 


DOUBLE,  MULTIPLE,  AND  BINARY  STARS.       391 


is  itself  double.  This  minute  pair  of  points,  capable  of  being  distin- 
guished as  double  only  by  tlie  most  perfect  eye  (without  the  tele- 
scope), is  really  composed  of  two  pairs 
of  stars  wide  apart,  with  a  group  of 
smaller  stars  between  and  around 
them.  The  figure  shows  the  appear- 
ance in  a  telescope  of  considerable 
power. 

Revolutions  of  Double  Stars — Binary 
Systems. — It  is  evident  that  if  stars 
physically  double  are  subject  to  the 
force  of  gravitation,  they  must  be 
revolving  around  each  other,  as  the 
Earth  and  planets  revolve  around  the 
Sun,  else  they  would  be  drawn  together  FlG-  202. -THE  QUADRUPLE 

,  DTAR    €   IjYR^E. 

as  a  single  star. 

The  method  of  determining  the  period  of  revolution  of  a  pair  of 
stars,  A  and  B,  is  illustrated  by  the  figure,  whi,h  is  supposed  to  rep- 
resent the  field  of  view  of  an  inverting  telescope  pointed  toward  the 

south.  The  arrow  shows  the 
direction  of  the  apparent  diur- 
nal motion.  The  telescope  is 
pointed  so  that  the  brighter  star 
is  in  the  centre  of  the  field. 
The  angle  of  position  of  the 
smaller  star  (NAB)  is  measured 
by  means  of  a  divided  ciicle, 
and  their  distance  apart  (AB)  is 
measured  with  the  micrometer 
(see  page  141)  at  the  same  time. 
If,  by  measures  of  this  sort, 
extending  through  a  series  of 
years,  the  distance  or  position- 
angle  of  a  pair  of  stars  is  found 
to  change  periodically,  it  sliows 
that  one  star  is  revolving  around 
the  other.  Such  a  pair  is  called 
a  binary  star  or  Unary  system. 
The  only  distinction  that  we 

can  make  between  binary  systems  and  ordinary  double  stars  is 
founded  on  the  presence  or  absence  of  this  observed  motion.  It  is 
probable  that  nearly  all  the  very  close  double  stars  are  really  binary 


FIG. 


203.— POSITION  ANGLE  OF  A 
DOUBLE  STAR. 


392  ASTRONOMY. 

systems,  but  that  many  hundreds  of  years  are  required  to  perform 
a  revolution  in  some  instances,  so  that  their  motion  has  not  yet  been 
detected. 

Certain  pairs  of  binary  stars  whose  components  are  entirely  too 
close  to  be  separable  by  the  telescope  have  been  discovered  by  the 
spectroscope.  If  two  stars,  A  and  B,  are  binary,  and  therefore  re- 
volving in  orbits,  they  will  sometimes  be  in  this  position  to  an  ob- 
server on  the  Earth,  thus  : 

AB 

T 

Earth. 

If  they  are  too  close  to  be  separated  by  the  telescope,  still  the  spec- 
trum of  the  pair  will  show  the  lines  of  both  stars.  That  is,  certain 
of  the  spectrum  lines  will  appear  double.  At  other  times  one  star 
will  be  behind  the  other,  as  seen  from  the  Earth,  thus  : 

B 
A 

1 

Earth. 

and  the  spectrum  lines  will  be  seen  single.  If  changes  like  these 
occur  periodically,  as  they  do,  then  the  orbit  of  one  star  about  the 
other  can  be  calculated.  In  this  way  a  number  of  "  spectroscopic 
binary  stars  "  has  been  found.  The  star  Zeta  Ursce  Majoris  (Mizar) 
(see  Fig.  95)  is  a  binary  of  this  class,  whose  period  is  about  52  days. 
The  mass  of  this  system  is  about  40  times  the  Sun's  mass. 

The  existence  of  binary  systems  shows  that  the  law  of  gravitation 
includes  the  stars  as  well  as  the  solar  system  in  its  scope,  and  thus 
that  it  is  truly  universal. 

When  the  parallax  of  a  binary  star  is  known,  as  well  as  the  orbit, 
it  is  possible  to  compute  the  mass  of  the  binary  system  in  terms  of 
the  Sun's  mass.  It  is  an  important  fact  that  the  stars  of  such  binary 
systems  as  have  been  investigated  do  not  differ  very  greatly  in  mass 
from  our  Sun. 


CHAPTER  XXVI. 

NEBULA   AND   CLUSTERS. 

45.  Nebulae. — In  the  star-catalogues  of  PTOLEMY  and 
the  earlier  writers,  there  was  included  a  class  of  nebulous 
or  cloudy  stars,  which  were  in  reality  star-clusters.  They 
were  visible  to  the  naked  eye  as  masses  of  soft  diffused 
light  like  parts  of  the  Milky  Way.  The  telescope  shows 
that  most  of  these  objects  are  clusters  of  stars. 

As  the  telescope  was  improved,  great  numbers  of  such 
patches  of  light  were  found,  some  of  which  could  be 
resolved  into  stars,  while  others  could  not.  The  latter 
were  called  nebulce  and  the  former  star-clusters. 

About  1656  HUYGHEXS  described  the  great  nebula  of 
Orion,  one  of  the  most  remarkable  and  brilliant  of  these 
objects.  It  is  just  visible  to  the  naked  eye  as  a  cloudiness 
about  the  middle  star  of  the  sword  of  Orion  (a  line  from 
the  r  of  Orion  in  Fig.  204  to  the  r  of  Eridanus  passes 
through  the  nebula).  The  student  should  look  for  this 
nebula  with  the  eye  on  a  clear  winter's  night.  An  opera- 
glass  will  show  the  nebulosity  distinctly;  but  a  telescope  is 
needed  to  show  it  well.  Sir  WILLIAM  HERSCHEL  with  his 
great  telescopes  first  gave  proof  of  the  enormous  number 
of  these  masses.  In  1786  he  published  a  catalogue  of  one 
thousand  new  nebulae  and  clusters.  This  was  followed  in 
1789  by  a  catalogue  of  a  second  thousand,  and  in  1802  by 
a  third  catalogue  of  five  hundred  new  objects  of  this  class. 
Sir  JOHN  HERSCHEL  added  about  two  thousand  more 

393 


394 


ASTRONOMY. 


nebulae.     About  nine  thousand  nebulae,  mostly  very  faint, 
are  now  known. 

Classification  of  Nebulae  and  Clusters.— In  studying  these  objects,  the 
first  question  we  meet  is  this  :  Are  all  these  bodies  clusters  of  stars 


FIG. 


204  —THE  CONSTELLATION  ORION  AS  SEEN  WITH  THE 
NAKED  EYE. 


which  look  diffused  only  because  they  are  so  distant  that  our  tele- 
scopes cannot  distinguish  the  separate  stars?  or  are  some  of  them 
in  reality  what  they  seem  to  be  ;  namely,  diffused  masses  of  matter? 
In  his  early  memoirs,  Sir  WILLIAM  HERSCHEL  took  the  first  view. 
He  considered  the  Milky  Way  as  nothing  but  a  congeries  of  stars,  and 
all  nebulae  seemed  to  be  but  stellar  clusters,  so  distant  as  to  cause  the 
individual  stars  to  disappear  in  a  general  milkiness  or  nebulosity. 


AND  CLUSTERS.  395 

In  1791,  however,  he  discovered  a  nebulous  star  (properly  so  called) 
— that  is,  a  star  which  was  undoubtedly  similar  to  the  surrounding 
stars,  and  which  was  encompassed  by  a  halo  of  nebulous  light.  His 
reasoning  on  this  discovery  is  instructive. 

He  says :  "  Supposing  the  nucleus  and  halo  to  be  connected,  we 
may,  first,  suppose  the  whole  to  be  of  stars,  in  which  case  either  the 
nucleus  is  enormously  larger  than  other  stars  of  its  stellar  magnitude, 


FIG.  205.— SPI-RAL  NEBULA. 

or  the  envelope  is  composed  of  stars  indefinitely  small ;  or,  second, 
we  must  admit  that  the  star  is  involved  in  a  shining  fluid  of  a  nature 
totally  unknown  to  us. 

"  The  shining  fluid  might  exist  independently  of  stars.  The  light 
of  this  fluid  is  no  kind  of  reflection  from  the  star  in  the  centre.  If 
this  matter  is  self-luminous,  it  seems  more  fit  to  produce  a  star  by  its 
condensation  than  to  depend  on  the  star  for  its  existence." 

This  was  the  first  exact  statement  of  the  idea  that,  beside  stars  and 


396 


ASTRONOMY. 

H 


NEBULA  AND   CLUSTERS.  397 

star-clusters,  we  have  in  the  universe  a  totally  distinct  series  o^  ob- 
jects, probably  much  more  simple  in  their  constitution.  Observations 
on  the  spectra  of  these  bodies  have  entirely  confirmed  the  conclusions 
of  HERSCHEL.  The  spectroscope  shows  that  the  true  nebulas  are 
gaseous. 

Nebulae  and  clusters  are  divided  into  classes.  A  planetary  nebula 
is  circular  or  elliptic  in  shape,  with  a  definite  outline  like  a  planet. 
Spiral  nebulae,  are  those  whose  convolutions  have  a  spiral  shape.  This 
class  is  quite  numerous. 

The  different  kinds  of  nebulae  and  clusters  will  be  better  under- 
stood irom  the  cuts  and  descriptions  which  follow  than  by  formal 


FIG.  207. — THE  MOON  PASSING  NEAR  THE  PLEIADES. 

definitions.  It  must  be  remembered  that  there  is  an  almost  infinite 
variety  of  such  shapes.  The  real  shape  of  the  nebula  in  space  ap- 
pears to  us  much  changed  by  perspective. 

Vast  areas  of  the  sky  are  covered  with  faint  nebulosity. 

Star-clusters. — The  most  noted  of  all  the  clusters  is  the  Pleiades, 
which  may  be  seen  during  the  winter  months  to  the  northwest  of  the 
constellation  Taurus  The  average  naked  eye  can  easily  distinguish 
six  stars  within  it,  but  under  favorable  conditions  ten,  eleven,  twelve, 
or  more  stars  can  be  counted.  With  the  telescope,  several  hundred 
stars  are  seen. 

The  clusters  represented  in  Figs.  208  and  209  are  good  examples  of 
their  classes.  The  first  is  globular  and  contains  several  thousand 
small  stars.  The  second  is  a  cluster  of  about  200  stars,  of  magni- 
tudes varying  from  the  ninth  to  the  thirteenth  and  fourteenth,  in 
which  the  brighter  stars  are  scattered. 


398  ASTRONOMY. 

Clusters  are  probably  subject  to  central  powers  or  forces.  This 
was  seen  by  Sir  WILLIAM  HERSCHEL  in  1789.  He  says  : 

"  Not  only  were  round  nebulae  and  clusters  formed  by  central 
powers,  but  likewise  every  cluster  of  stars  or  nebula  that  shows  a 
gradual  condensation  or  increasing  brightness  toward  a  centre. 

"  Spherical  clusters  are  probably  not  more  different  in  size  among 
themselves  than  different  individuals  of  plants  of  the  same  species. 
As  it  has  been  shown  that  the  spherical  figure  of  a  cluster  of  stars  is 
owing  to  central  powers,  it  follows  that  those  clusters  which,  cceteris 
paribus,  are  the  most  complete  in  this  figure  must  have  been  the 
longest  exposed  to  the  action  of  these  causes. 


FIG.  208.— GLOBULAR  CLUSTER. 

"The  maturity  of  a  sidereal  system  may  thus  be  judged  from  the 
disposition  of  the  component  parts. 

"Though  we  cannot  see  any  individual  nebula  pass  through  all  its 
stages  of  life,  we  can  select  particular  ones  in  each  peculiar  stage," 
and  thus  obtain  a  single  view  of  their  entire  course  of  development. 

Spectra  of  Nebulae  and  Clusters.— In  1864,  five  years  after  the  in- 
vention of  the  spectroscope,  the  examination  of  the  spectra  of  the 
nebula3  by  Sir  WILLIAM  HUGGINS  led  to  the  discovery  that  while  the 
spectra  of  stars  were-  invariably  continuous  and  crossed  with  dark 
lines  similar  to  those  of  the  solar  spectrum,  those  of  many  nebulae 
were  discontinuous,  showing  these  bodies  to  be  composed  of  glowing 
gas.  The  nebulae  have  proper  motions  just  as  do  the  stars.  The 
great  nebula  of  Orion  is  moving  away  from  the  Sun  eleven  miles 
every  second. 


NEBULA  AND   CLUSTERS.  399 

The  spectrum  of  most  clusters  is  continuous,  indicating  that  the 
individual  stars  are   truly  stellar  in  their  nature.     In  a  few  cases, 


FIG  201).  — COMPRESSED  CLUSTER. 

however,  clusters  are  composed  of  a  mixture  of  nebulosity  (usually 
near  their  centre)  and  of  stars,  and  the  spectrum  in  such  cases  is 
compound  in  its  nature,  so  as  to  indicate  radiation  from  both  gaseous 
and  solid  matter. 


CHAPTER  XXVII. 

SPECTRA   OF   FIXED  STARS.* 

46.  Stellar  spectra  are  found  to  be,  in  the  main,  similar 
to  the  solar  spectrum;  i.e.,  composed  of  a  continuous  band 
of  the  prismatic  colors,  across  which  dark  lines  or  bands 
are  laid,  the  latter  being  fixed  in  position.  These  results 
show  the  fixed  stars  to  resemble  our  own  Sun  in  general 
constitution,  and  to  be  composed  of  an  incandescent 
nucleus  surrounded  by  a  gaseous  and  absorptive  atmosphere 
of  lower  temperature  containing  the  vapors  of  metals, 
etc.— iron,  magnesium,  hydrogen,  etc.  The  atmosphere 
of  many  stars  is  quite  different  in  constitution  from  that  of 
the  Sun,  as  is  shown  by  the  different  position  and  intensity 
of  the  various  dark  lines  that  are  due  to  the  absorptive 
action  of  the  atmospheres  of  the  stars. 

Different  Types  of  Stars. — In  a  general  way  the  spectra  of  all  stars 
are  similar.  All  of  them  are  bodies  of  the  same  general  kind  as  the 
San.  Yet  there  are  characteristic  differences  between  star  and  star, 
and  certain  large  groups  into  which  stars  can  be  classified — certain 
types  of  stellar  spectra.  It  is  probable  that  these  different  types  rep- 
resent different  phases  in  the  life-history  of  a  star.  Of  two  stars  of 
the  same  size  and  general  constitution  the  whitest  is  probably  the 
hottest  and  the  youngest ;  the  reddest  is  probably  the  coolest  and 
oldest.  The  hottest  stars  have  the  simplest  spectra ;  the  red  stars 
have  complicated  spectra  and  are  often  variable.  The  bright  stars 
of  the  constellation  of  Orion  have  spectra  of  the  simplest  type — their 
atmospheres  are  mainly  made  up  of  helium  and  hydrogen  gases. 
Stars  like  Sirius  have  little  helium  in  their  atmospheres,  but  much 

*  See  Appendix. 

400 


SPECTRA   OF  FIXED  STARS.  401 

hydrogen  and  a  little  calcium.  Stars  like  Procyon  have  hydrogen 
and  calcium  and  magnesium  in  marked  quantities,  besides  other  me- 
tallic lines.  Stars  like  Arcturus  are  characterized  by  many  metallic 
lines  in  their  spectra,  such  as  those  of  iron.  Our  Sun  belongs  to 
this  class.  Stars  with  considerably  less  extensive  hydrogen  atmos- 
pheres and  with  considerably  more  metallic  vapors  surrounding 
them  form  the  next  class  (like  Alpha  Orionis,  Alpha  Herculis  and 
the  variable  star  Mira  Cetis).  The  red  stars,  none  of  which  are  very 
bright,  and  most  of  which  are  variable,  form  the  last  type. 

It  appears  that  the  stars  can  be  arranged  in  classes  corresponding 
to  diminishing  temperatures.  The  hottest  stars  have  extensive  hy- 
drogen atmospheres,  simple  in  constitution.  They  are  analogous  to 
nebulae  in  many  respects  and  probably  are  condensed  from  nebulous 
masses.  As  a  star  grows  older  and  cooler  its  spectrum  grows  more 
unlike  a  nebulous  spectrum,  more  complex,  more  individual,  so  to 
speak.  After  passing  through  a  stage  like  that  of  our  Sun  it 
reaches  the  stage  of  pronounced  variability,  like  the  red  stars,  and 
finally  becomes  a  "dark  star"  like  the  companion  to  Algol,  for 
example. 

Stellar  Evolution :  An  irregular  and  widely  extended  nebula  sub- 
ject to  gravitating  forces  tends  to  become  a  spherical  mass  ;  spherical 
masses  of  nebulosity  subject  to  central  powers  tend  to  become  more 
condensed  and  to  form  nuclei  at  their  centres.  It  appears  to  be 
likely  that  such  nebulae  may  condense  still  further  into  stars.  Stars 
very  hot  and  white  go  through  a  cycle  of  changes,  and  after  losing 
all  their  light  and  heat  become  "dark  stars."  This  is,  in  general, 
the  final  stage.  If,  however,  two  stellar  systems  moving  through 
space  should  collide,  all  the  bodies  of  both  systems  would  be  quickly 
raised  to  very  high  temperatures,  and  in  this  way  a  "dark  star" 
might  be  re-created  and  begin  a  new  cycle  of  existence.  If  a  dark 
star  like  the  Earth,  for  example,  were  to  be  suddenly  raised  to  a 
very  high  temperature  it  would  become  a  gaseous  body — a  miniature 
Sun,  for  example.  It  is  probable  that  the  phenomena  of  some  of 
the  "  new  stars  "  are  to  be  explained  in  this  way. 

Motion  of  Stars  in  the  Line  of  Sight. —  Spectroscopic 
observations  of  stars  not  only  give  information  in  regard  to 
their  chemical  and  physical  constitution,  but  have  been 
applied  so  as  to  determine  approximately  the  velocity  in 
miles  per  second  with  which  the  stars  are  approaching  to 
or  receding  from  the  Earth  along  the  line  joining  Earth 


402  ASTRONOMY. 

and  star  (the  line  of  sight).     The  theory  of  such  a  de- 
termination is  briefly  as  follows: 

In  the  solar  spectrum  we  find  a  group  of  dark  lines,  as  a,  b,  c, 
which  always  maintain  their  relative  position.  From  laboratory  ex- 
periments, we  can  show  that  the  three  bright  lines  of  incandescent 
hydrogen  (for  example)  have  always  the  same  relative  position  as  the 
solar  dark  lines  a,  b,  c.  From  this  it  is  inferred  that  the  solar  dark 
lines  are  due  to  the  presence  of  hydrogen  in  the  absorptive  atmosphere 
of  the  Sun. 

Now,  suppose  that  in  a  stellar  spectrum  we  find  three  dark  lines, 
a',  b' ,  c',  whose  relative  position  is  exactly  the  same  as  that  of  the 
solar  lines  a,  b,  c.  Not  only  is  their  relative  position  the  same,  but 
the  characters  of  the  lines  themselves,  so  far  as  the  fainter  spectrum 
of  the  star  will  allow  us  to  determine  them,  are  also  similar  ;  that  is, 
a'  and  a,  b'  and  b,  c'  and  c  are  alike  as  to  thickness,  blackness,  nebu- 
losity of  edges,  etc.,  etc.  From  this  it  is  inferred  that  the  star  con- 
tains in  its  atmosphere  the  substance  whose  existence  has  been  shown 
in  the  Sun — hydrogen,  for  example. 

If  we  contrive  an  apparatus  by  which  the  stellar  spectrum  is  seen 
in  the  lower  half,  say,  of  the  eyepiece  of  the  spectroscope,  while  the 
spectrum  of  hydrogen  is  seen  just  above  it.  we  find  in  some  cases  this 
remarkable  phenomenon.  The  three  dark  stellar  lines,  a ',  b',  c',  in- 
stead of  being  exactly  coincident  with  the  three  hydrogen  lines  a,  b, 
c,  are  seen  to  be  all  thrown  to  one  side  or  the  other  by  a  like  amount ; 
that  is,  the  whole  group  a',  b',  c',  while  preserving  its  relative  dis- 
tances the  same  as  those  of  the  comparison  group  a,  b,  c,  is  shifted 
toward  either  the  violet  Or  red  end  of  the  spectrum  by  a  small  yet 
measurable  amount.  Repeated  experiments  by  different  instruments 
and  observers  always  show  a  shifting  in  the  same  direction,  and  of 
like  amount.  The  figure  shows  a  shifting  of  the  F  line  in  the 
spectrum  of  Sirius,  compared  with  one  fixed  line  of  hydrogen.  The 
bright  line  of  hydrogen  is  nearer  to  one  side  of  the  dark  line  in  the 
stellar  spectrum  than  to  the  other. 

This  displacement  of  the  spectral  lines  is  accounted  for  by  a  motion 
of  the  star  toward  or  from  the  Earth.  It  is  shown  in  Physics  that  if 
the  source  of  the  light  which  gives  the  spectrum  a',  b',  c'  is  moving 
away  from  the  Earth,  this  group  will  be  shifted  toward  the  red  end 
of  the  spectrum  ;  if  toward  the  Earth,  then  the  whole  group  will  be 
shifted  toward  the  blue  end.  The  amount  of  this  shifting  depends 
upon  the  velocity  of  recession  or  approach,  and  this  velocity  in  miles 
per  second  can  be  calculated  from  the  measured  displacement.  This 
has  already  been  done  for  many  stars. 


SPECTRA   OF  FIXED  STARS.  403 

The  principle  upon  .which  the  calculation  is  made  can 
be  understood  by  an  analogy  drawn  from  the  phenomena 
of  sound.  Every  one  who  has  ridden  in  a  railway  train  has 
noticed  that  the  bell  of  a  passing  engine  does  not  always  give 
out  the  same  note.  As  the  two  trains  approach  the  sound  of 
the  bell  is  pitched  higher,  and  as  they  separate  after  passing 
the  sound  of  the  bell  is  lower.  It  is  certain  that  the  driver 
of  the  passing  engine  always  hears  his  bell  give  out  one  and 
the  same  note.  The  explanation  of  this  phenomenon  is  as 
follows:  the  bell  of  the  passing  engine  gives  out  the  note 


FIG.  210.—^  LINE  OF  HYDROGEN  SUPERPOSED  ON  THE  SPECTRUM 
ov  Siuius  (K#). 

C  (the  middle  C  of  the  pianoforte)  let  us  say.  That  is 
it  gives  oat  512  vibrations,  sound-waves,  in  every  second. 
Any  sonorous  body  giving  out  512  waves  per  second  makes 
the  note  C.  If  more  than  512  sound-waves  reach  the  ear 
in  a  second  the  note  is  higher — (7jf  for  example.  If  fewer 
than  512  waves  reach  the  ear  in  a  second  the  note  is  lower 
— Co  for  example.  The  engineer  hears  512  vibrations 
every  second.  The  note  of  his  bell  is  C'fcj.  All  the  air 
around  him  is  filled  with  sound-waves  of  this  frequency. 


404:  ASTRONOMY. 

The  traveller  approaching  the  bell  hears  the  512  vibrations 
given  out  by  the  bell  every  second,  and  also  other  vibrations 
that  his  swiftly  moving  train  meets — the  note  of  the  bell  to 
him  is  C%  let  us  say,  because  his  ear  collects  more  than  512 
vibrations  every  second.  The  traveller  receding  from  the 
bell  hears  fewer  than  512  vibrations  per  second.  Not  all 
of  the  waves  given  out  by  the  bell  can  overtake  him  as  he 
moves  swiftly  away — the  note  of  the  bell  is  to  him  C\> — let 
us  say. 

The  case  is  the  same  for  light-waves.  The  F  line  of 
hydrogen  gives  out  in  the  laboratory  a  certain  number  of 
waves  per  second.  If  a  star  is  at  rest  with  respect  to  the 
Earth  just  as  many  waves  reach  the  observer's  eye  from  the 
F  line  of  the  star  as  reach  it  from  the  F  line  of  a  compari- 
son-spectrum of  hydrogen.  Both  sources  of  light  are  at 
rest  with  respect  to  him.  If  he  is  moving  swiftly  towards 
the  star  his  eye  receives  not  only  the  waves  sent  out  by  the 
star,  but  also  all  those  that  he  overtakes.  If  he  is  moving 
swiftly  away  from  the  star  his  eye  receives  fewer  waves  than 
the  star  sends  out  because  not  all  of  them  can  overtake 
him.  (It  is  as  if  the  F%  of  the  star  became  jPJ  in  one 
case,  Ffr  in  the  other.)  A  shifting  of  the  star-line  towards 
the  violet  end  of  the  spectrum  indicates  an  approach  of  the 
Earth  to  the  star;  a  shifting  towards  the  red  end  indicates 
a  recession.  The  velocity  of  the  motion  of  approach  or 
recession  is  proportional  to  the  amount  of  the  shifting.  It 
is  by  a  principle  of  this  kind  that  we  can  calculate  from  the 
observed  shifting  of  lines  in  the  stellar  spectrum  the 
velocity  with  which  the  Earth  is  approaching  a  star,  or 
receding  from  it. 

Motion  of  the  Solar  System  in  Space. — If  observation 
shows  that  the  Earth  is  approaching  a  star  at  the  rate  of 
40  miles  per  second,  we  know  that  the  Sun  and  all  the 
planets  must  be  moving  towards  that  star,  since  the  Earth 
moves  in  her  orbit  only  18  miles  per  second.  By  making 


SPECTRA   OF  FIXED  STARS. 


405 


allowance  for  the  Earth's  motion,  the  exact  velocity  of  the 
Sun  towards  the  star  can  be  calculated.  The  Sun  carries 
all  his  family — all  the  planets — with  him  as  he  moves 
through  space.  Astronomers  are  now  engaged  in  solving, 
by  spectroscopic  means,  the  problem  of  how  fast  the  solar 
system  is  moving  in  space,  and  in  what  direction  it  is 
moving. 

The  method  employed  is  somewhat  as  follows  :  A  large 
number  of  stars  is  spectroscopically  observed  and  the  ve- 
locity with  which  the  Sun  is  approaching  each  separate 
star  is  accurately  determined. 


FIG.  211. 

Suppose  the  observations  to  show  that  the  Sun  (O)  is  ap- 
proaching the  group  of  stars  A  with  an  average  velocity  of 
12  miles  per  second ;  that  it  is  receding  from  the  group  of 
stars  B  (180°  away  from  A — opposite  to  A  in  the  celestial 
sphere)  at  the  same  velocity ;  then  it  follows  that  the  Sun 
with  the  whole  solar  system  is  moving  through  space  to- 
wards A  with  a  velocity  of  12  miles  per  second. 


406  ASTRONOMY. 

Some  of  the  stars  of  group  A  may  be  moving  towards  the 
Sun;  some  of  them  may  be  moving  away  from  the  Sun;  if 
a  great  many  stars  are  contained  in  the  group  their  average 
motion  with  respect  to  the  Sun  will  be  zero:  there  is  no 
reason  to  suppose  that  stars  in  general  have  any  tendency 
to  move  towards  our  Sun  or  away  from  it.  Groups  of  stars 
at  C  and  D  and  all  around  the  celestial  sphere  are  observed 
in  the  same  way,  and  the  final  result  is  made  to  depend  on 
air  the  observed  velocities.  Researches  like  this  are  in 
progress  at  Potsdam,  Paris,  at  the  Lick  Observatory,  and 
elsewhere.  Final  conclusions  have  not  yet  been  reached. 
All  that  can  now  be  said  is  that  the  solar  system  is  moving 
towards  a  point  near  to  the  bright  star  Alpha  LyrcB  with  a 
velocity  of  about  12  miles  per  second.  It  will  require 
some  years  yet  to  reach  final  values.  So  far  as  we  know 
the  solar  motion  is  uniform  and  in  a  straight  line. 


CHAPTER   XXVIII. 

COSMOGONY. 

47.  A  theory  of  the  operations  by  which  the  physical 
universe  received  its  present  form  and  arrangement  is  called 
Cosmogony.  This  subject  does  not  treat  of  the  origin  of 
matter,  but  only  of  its  transformations. 

Three  systems  of  Cosmogony  have  prevailed  at  different 
times : 

(1)  That  the  universe  had  no  beginning,  but  existed  from 
eternity  in  the  form  in  which  we  now  see  it.     This  was  the 
view  of  the  ancients. 

(2)  That  it  was  created  in  its  present  shape  in  six  days. 
This  view  is  based  on  the  literal  sense  of  the  words  of  the 
Old  Testament.     Theological  commentators  have  assumed 
that  it  was  created  "out  of  nothing,"  but  the  Scripture 
does  not  say  so. 

(3)  That  it  came  into  its  present  form  through  an  ar- 
rangement of  previously  existing  materials  which  were  be- 
fore "  without  form  and  void."     This  maybe  called  the 
evolution  theory.     No  attempt  is  made  to  explain  the  ori- 
gin of  the  primitive  matter.     The  theory  simply  deals  with 
its  arrangement  and  changes. 

The  scientific  discoveries  of  modern  times  show  conclu- 
sively that  the  universe  could  not  always  have  existed  in 
its  present  form ;  that  there  was  a  time  when  the  materials 
composing  it  were  masses  of  glowing  vapor,  and  that  there 
will  be  a  time  when  the  present  state  of  things  will  cease. 
Geology  proves  beyond  a  doubt,  that  the  arrangement  of 

407 


408  ASTRONOMY. 

the  primitive  matter  to  form  a  habitable  Earth  has  required 
millions  of  years,  and  Anthropology  proves  also  beyond  a 
doubt,  that  the  Earth  has  been  inhabited  by  men  for  many 
thousands.  It  was  not  until  the  latter  half  of  the  XVIII 
century  that  such  opinions  could  be  held  without  fear  of 
persecution,  for  the  lesson  "  that  a  scientific  fact  is  as  sacred 
as  a  moral  principle  "  has  only  been  fully  learned  within 
the  last  half  century. 

An  explanation  of  the  processes  through  which  the  Earth 
and  all  the  planets  came  into  their  present  forms  was  first 
propounded  by  the  philosophers  SWEDENBORG,  KANT,  and 
LAPLACE,  and,  although  since  greatly  modified  in  detail, 
their  fundamental  views  are,  in  the  main,  received.  The 
nebular  hypotheses  proposed  by  these  philosophers  all  start 
with  the  statement  that  the  Earth  and  Planets,  as  well  as 
the  Sun,  were  once  a  fiery  mass. 

It  is  certain  that  the  Earth  has  not  received  any  great  supply  of 
heat  from  outside  since  the  early  geological  ages,  because  such  an 
accession  of  heat  at  the  Earth's  surface  would  have  destroyed  all  life, 
and  even  melted  all  the  rocks.  Therefore,  whatever  heat  there  is  in 
the  interior  of  the  Earth  must  have  been  there  from  before  the  com- 
mencement of  life  on  the  globe,  and  remained  through  all  geological 
ages. 

The  interior  of  the  Earth  is  very  much  hotter  than  its  surface,  and 
hotter  than  the  celestial  spaces  around  it.  It  is  continually  losing 
heat,  and  there  is  no  way  in  which  the  losses  are  made  up.  We 
know  by  the  most  familiar  observation  that  if  any  object  is  hot  inside, 
the  heat  will  work  its  way  through  to  the  surface.  Therefore,  since 
the  Earth  is  a  great  deal  hotter  at  the  depth  of  50  miles  than  it  is  at 
the  surface,  and  much  hotter  at  500  miles  than  at  50,  heat  must  be 
continually  coming  to  the  surface.  On  reaching  the  surface,  it  must 
be  radiated  off  into  space,  else  the  surface  would  have  long  ago  be- 
come as  hot  as  the  interior. 

Moreover,  this  loss  of  heat  must  have  been  going  on  since  the  be- 
ginning, or  at  least  since  a  time  when  the  surface  was  as  hot  as  the 
interior.  Thus,  if  we  reckon  backward  in  time,  we  find  that  there 
must  have  been  more  and  more  heat  in  the  Earth  the  further  back  we 
go,  so  that  we  reach  a  time  when  the  Earth  was  so  hot  as  to  be 


COSMOGONY.  409 

molten,  and  finally  reach  a  time  when  it  was  so  hot  as  to  be  a  mass  of 
fiery  vapor. 

The  Sun  is  cooling  off  like  the  Earth,  only  at  an  incomparably  more 
rapid  rate.  The  Sun  is  constantly  radiating  heat  into  space,  and,  so 
far  as  we  know,  receiving  none  back  again.  A  very  small  portion  of 
this  heat  reaches  the  Earth,  and  on  this  portion  depends  the  existence 
of  life  and  motion  on  the  Earth's  surface.  If  our  supply  of  solar  heat 
were  to  be  taken  away,  all  life  on  the  Earth  would  cease.  The 
quantity  of  heat  which  strikes  the  Earth  is  only  about  2Tnnnnn>FffT>  °^ 
that  which  the  Sun  radiates.  This  fraction  expresses  the  ratio  of  the 
apparent  surface  of  the  Earth,  as  seen  from  the  Sun,  to  that  of  the 
whole  celestial  sphere. 

Since  the  Sun  is  constantly  losing  heat,  it  must  have  had  more  heat 
yesterday  than  it  has  to-day  ;  more  two  days  ago  than  it  had  yester- 
day; and  so  on.  The  further  we  go  back  in  time,  the  hotter  the  Sun 
must  have  been.  Since  we  know  that  heat  expands  all  bodies,  it  fol- 
lows that  the  Sun  must  have  been  larger  in  past  ages  than  it  is  now, 
and  we  can  calculate  the  size  of  the  Sun  at  any  past  time. 

Thus  we  are  led  to  the  conclusion  that  there  must  have  been  a  time 
when  the  Sun  filled  up  the  whole  of  the  space  now  occupied  by  the 
planets.  It  must  then  have  been  a  very  rare  mass  of  glowing  vapor. 
The  planets  could  not  then  have  existed  separately,  but  must  have 
formed  a  part  of  this  mass  of  vapor.  The  glowing  vapor — "  a  fiery 
mist" — was  the  material  out  of  which  the  solar  system  was  formed. 

The  same  process  may  be  continued  into  the  future.  Since  the  Sun 
by  its  radiation  is  constantly  losing  heat,  it  must  grow  cooler  and 
cooler  as  ages  advance,  and  must  finally  radiate  so  little  heat  that  fife 
and  motion  can  no  longer  exist  on  our  globe. 

It  is  a  noteworthy  confirmation  of  this  hypothesis  that  the  revolu- 
tions of  all  the  planets  around  the  Sun  take  place  in  the  same  direc- 
tion and  in  nearly  the  same  plane.  This  similarity  among  the  differ- 
ent bodies  of  the  solar  system  must  have  had  an  adequate  cause.  The 
Sun  and  planets  were  once  a  great  mass  of  vapor,  larger  than  the 
present  solar  system,  that  revolved  on  its  axis  in  the  same  plane  in 
which  the  planets  now  revolve. 

The  spectroscope  shows  the  nebulae  to  be  masses  of  glowing  vapor. 
We  thus  actually  see  matter  in  the  celestial  spaces  under  the  very 
form  in  which  the  nebular  hypothesis  supposes  the  matter  of  our  solar 
system  to  have  once  existed.  Some  of  these  nebulae  now  have  the 
very  form  that  the  nebular  hypothesis  assigns  to  the  solar  nebula  in 
past  ages.  (See  the  frontispiece.)  The  nebulas  are  gradually  cooling. 
The  process  of  cooling  must  at  length  reach  a  point  when  they  will 


410  ASTRONOMY. 

cease  to  be  vaporous  and  will  condense  into  objects  like  stars  and 
planets.  All  the  stars  must,  like  the  Sun,  be  radiating  heat  into  space. 

The  telescopic  examination  of  the  planets  Jupiter  and  Saturn  shows 
that  changes  on  their  surfaces  are  constantly  going  on  with  a  rapidity 
and  violence  to  which  nothing  on  the  surface  of  our  Earth  can  com- 
pare. Such  operations  can  be  kept  up  only  through  the  agency  of 
heat  or  some  equivalent  form  of  energy.  At  the  distance  of  Jupiter 
and  Saturn,  the  rays  of  the  Sun  are  entirely  insufficient  to  produce 
such  changes.  Jupiter  and  Saturn  must  be  hot  bodies,  and  must 
therefore  be  cooling  off  like  the  Sun,  stars,  and  Earth. 

These  and  many  other  allied  facts  lead  to  the  conclusion  that  most 
bodies  of  the  universe  are  hot,  and  are  cooling  off  by  radiating  their 
heat  into  space. 

There  is  no  way  known  to  us  in  which  the  heat  radiated  by  the  Sun 
and  stars  might  be  collected  and  returned  to  them.  It  is  a  funda- 
mental principle  of  the  laws  of  heat  that  "  heat  can  never  pass  from 
a  cooler  to  a  warmer  body  " — that  a  body  can  never  grow  warmer  in 
a  space  that  is  cooler  than  the  body  itself. 

All  differences  of  temperature  tend  to  equalize  themselves,  and  the 
only  state  of  things  to  which  the  universe  can  tend,  under  its  present 
laws,  is  one  in  which  all  space  and  all  the  bodies  contained  in  space 
will  be  at  a  uniform  temperature,  and  then  all  motion  and  change  of 
temperature,  and  hence  the  conditions  of  vitality,  must  cease.  And 
then  all  such  life  as  ours  must  cease  also  unless  sustained  by  entirely 
new  methods. 

The  general  result  drawn  from  all  these  laws  and  facts 
is,  that  there  was  once  a  time  when  all  the  bodies  of  the 
universe  formed  either  a  single  mass  or  a  number  of  masses 
of  fiery  vapor,  having  slight  motions  in  various  parts,  and 
different  degrees  of  density  in  different  regions.  A  grad- 
ual condensation  around  the  centres  of  greatest  density  then 
took  place  in  consequence  of  the  cooling  and  the  mutual  at- 
traction of  the  parts,  and  thus  arose  a  number  of  separate 
nebulous  masses.  One  of  these  masses  formed  the  material 
out  of  which  the  Sun  and  planets  are  supposed  to  have 
been  formed.  It  was  probably  at  first  nearly  globular,  of 
nearly  equal  density  throughout,  and  endowed  with  a  very 
slow  rotation  in  the  direction  in  which  the  planets  now 


COSMOGONY.  411 

move.     As  it  cooled  off,  it  grew  smaller  and  smaller,  and 
its  velocity  of  rotation  increased  in  rapidity. 

The  rotating  mass  we  have  described  had  an  axis  around  which  it 
rotated,  and  an  equator  everywhere  90°  from  this  axis.  As  the  velocity 
of  rotation  increased,  the  centrifugal  force  also  increased.  This  force 
varies  as  the  radius  of  the  circle  described  by  any  particle  multiplied 
by  the  square  of  its  angular  velocity.  Hence  when  the  masses,  being 
reduced  to  half  the  radius,  rotated  four  times  as  fast,  the  centrifugal 
force  at  the  equator  would  be  increased  £  X  41,  or  eight  times.  The 
gravitation  of  the  mass  at  the  surface,  being  inversely  as  the  square 
of  the  distance  from  the  centre,  or  of  the  radius,  would  be  increased 
only  four  times.  Therefore,  as  the  masses  continued  to  contract,  the 
centrifugal  force  increased  more  rapidly  than  the  central  attraction. 
A  time  would  therefore  come  when  they  would  balance  each  other  at 
the  equator  of  the  mass. 

The  mass  would  then  cease  to  contract  at  the  equator,  but  at  the 
poles  there  would  be  no  centrifugal  force,  and  the  gravitation  of  the 
mass  would  grow  stronger  and  stronger  in  this  neighborhood. 

In  consequence  the  mass  would  at  length  assume  the 
form  of  a  lens  or  disk  very  thin  in  proportion  to  its  extent. 
The  denser  portions  of  this  lens  would  gradually  be  drawn 
toward  the  centre,  and  there  more  or  less  solidified  by 
cooling.  At  length,  solid  particles  would  begin  to  be 
formed  throughout  the  whole  disk.  These  would  grad- 
ually condense  around  each  other  and  form  a  single  planet, 
or  break  up  into  small  masses  and  form  a  group  of  planets. 
As  the  motion  of  rotation  would  not  be  altered  by  these 
processes  of  condensation,  these  planets  would  all  rotate 
around  the  central  part  of  the  mass,  which  condensed  to 
form  our  Sun. 

These  planetary  masses,  being  very  hot,  were  composed  of  a  central 
mass  of  those  substances  which  condensed  at  a  very  high  tempera- 
ture, surrounded  by  the  vapors  of  other  substances  which  were  more 
volatile.  We  know,  for  instance,  that  it  takes  a  much  higher  tem- 
perature to  reduce  lime  and  platinum  to  vapor  than  it  does  to  reduce 
iron,  zinc,  or  magnesium.  Therefore,  in  the  original  planets,  the 
limes  and  earths  would  condense  first,  while  many  other  metals  would 
still  remain  in  a  state  of  vapor. 


412  ASTRONOMY. 

Each  of  the  planetary  masses  would  rotate  more  rapidly  as  it  grew 
smaller,  and  would  at  length  form  a  mass  of  melted  metals  and  vapors 
in  the  same  way  as  the  larger  mass  out  of  which  the  Sun  and  planets 
were  formed.  These  separate  masses  would  then  condense  into  a 
planet,  with  satellites  revolving  around  it,  just  as  the  original  mass 
condensed  into  Sun  and  planets. 

At  first  the  planets  would  be  in  a  molten  condition,  each  shining 
like  the  Sun.  They  would,  however,  slowly  cool  by  the  radiation  of 
heat  from  their  surfaces.  So  long  as  they  remained  liquid,  the  sur- 
face, as  fast  as  it  grew  cool,  would  sink  into  the  interior  on  account 
of  its  greater  specific  gravity,  and  its  place  would  be  taken  by  hotter 
material  rising  from  the  interior  to  the  surface,  there  to  cool  off  in  its 
turn. 

There  would,  in  fact,  be  a  motion  something  like  that  which  occurs 
when  a  pot  of  cold  water  is  set  upon  the  fire  to  boil.  Whenever  a 
mass  of  water  at  the  bottom  of  the  pot  is  heated,  it  rises  to  the  sur- 
face, and  the  cool  water  moves  down  to  take  its  place.  Thus,  on  the 
whole,  so  long  as  the  planet  remained  liquid,  it  would  cool  off  equally 
throughout  its  whole  mass,  owing  to  the  constant  motion  from  the 
centre  to  the  circumference  and  back  again. 

A  time  would  at  length  arrive  when  many  of  the  earths  and  metals 
would  begin  to  solidify.  At  first  the  solid  particles  would  be  carried 
up  and  down  with  the  liquid.  A  time  would  finally  arrive  when  they 
would  become  so  large  and  numerous,  and  the  liquid  part  of  the  gen- 
eral mass  so  viscid,  that  their  motion  would  be  obstructed.  The 
planet  would  then  begin  to  solidify.  Two  views  have  been  enter- 
tained respecting  the  process  of  solidification. 

According  to  one  view,  the  whole  surface  of  the  planet  would 
solidify  into  a  continuous  crust,  as  ice  forms  over  a  pond  in  cold 
weather,  while  the  interior  was  still  in  a  molten  state.  The  interior 
liquid  could  then  no  longer  come  to  the  surface  to  cool  off,  and  could 
lose  no  heat  except  what  was  conducted  through  this  crust.  Hence 
the  subsequent  cooling  would  be  much  slower,  and  the  globe  would 
long  remain  a  mass  of  lava,  covered  over  by  a  comparatively  thin  solid 
crust  like  that  on  which  we  live. 

The  other  view  is  that,  when  the  cooling  attained  a  certain  stage, 
the  central  portion  of  the  globe  would  be  solidified  by  the  enormous 
pressure  of  the  superincumbent  portions,  while  the  exterior  was  still 
fluid,  and  that  thus  the  solidification  would  take  place  from  the 
centre  outward. 

It  is  still  an  unsettled  question  whether  the  Earth  is  now  solid  to 
its  centre,  or  whether  it  is  a  great  globe  of  molten  matter  with  a  com- 


COSMOGONY.  413 

paratively  thin  crust.  Astronomers  and  physicists  incline  to  the 
former  view  ;  some  geologists  to  the  latter  one.  Whichever  view 
may  be  correct,  it  appears  certain  that  there  are  lakes  of  lava  im- 
mediately beneath  the  active  volcanoes. 

It  must  be  understood  that  the  nebular  hypothesis  is  not 
a  perfectly  established  scientific  theory,  but  only  a  philo- 
sophical conclusion  founded  on  the  widest  study  of  nature, 
and  supported  by  many  otherwise  disconnected  facts.  The 
widest  generalization  associated  with  it  is  that,  so  far  as 
can  now  be  known,  the  universe  is  not  self-sustaining,  but 
is  a  kind  of  organism  which,  like  all  other  organisms  known 
to  us,  must  come  to  an  end  in  consequence  of  those  very 
laws  of  action  which  keep  it  going.  It  must  have  had  a 
beginning  within  a  certain  number  of  years  that  cannot 
yet  be  calculated  with  certainty,  but  which  cannot  in  any 
event  much  exceed  20,000,000,  and  it  must  end  in  a  system 
of  cold,  dead  globes  at  a  calculable  time  in  the  future, 
when  the  Sun  and  stars  shall  have  radiated  away  all  their 
heat,  unless  it  is  re-created  by  the  action  of  forces  at  present 
unknown  to  science. 

It  must  be  carefully  noted  that  these  conclusions,  which 
are  correct  in  the  main,  relate  entirely  to  the  transformations 
of  matter  in  the  past  and  future  time,  and  say  nothing  as  to 
its  origin.  The  original  nebula  must  have  contained  all  the 
matter  now  in  the  universe,  and  it  must  have  possessed,  po- 
tentially, all  the  energy  now  operative  as  light,  heat,  etc., 
besides  the  vast  stores  of  energy  that  have  been  expended  in 
past  ages.  The  process  by  which  the  physical  universe  was 
transformed  from  one  condition  to  a  later  one  is  the  subject 
of  the  nebular  hypothesis.  The  field  of  physical  science  is 
a  limited  one,  although  within  that  field  it  deals  with  pro- 
found problems.  Astronomy  has  nothing  to  say  on  the 
question  of  the  origin  of  matter  nor  on  the  vastly  more  im- 
portant questions  as  to  the  origin  of  life,  intelligence, 
wisdom,  affection. 


CHAPTER  XXIX. 

PRACTICAL   HINTS   ON   OBSERVING. 

48.  A  few  Practical  Hints  on  Making  Observations. — 
Lists  of  a  few  Interesting  Celestial  Objects. — Stars,  Double 
Stars,  Variable  Stars,  Nabulae,  Clusters. — Maps  of  the  Stars. 

— In  the  paragraphs  that  follow  a  few  hints  are  given  for  the 
benefit  of  the  student  who  wishes  to  begin  to  make  simple 
observations  for  himself.  Long  and  detailed  instructions 
might  be  set  down  which  would  perhaps  save  many  mis- 
takes. But  it  is  by  mistakes  made  and  corrected  that  one 
learns.  A  genius  is  a  person  who  never  makes  the  same 
mistake  twice.  The  rest  of  mankind  must  educate  them- 
selves by  slow  and  patient  correction  of  the  errors  they 
commit.  Therefore  only  enough  is  here  set  down  to  start 
the  student  on  his  way.  It  will  depend  on  himself  and  his 
opportunities  how  far  he  goes. 

Observations  of  the  Planets.— The  accurate  places  of  the  planets  are 
printed  in  the  Nautical  Almanac  (address  Nautical  Almanac  office, 
Navy  Department,  Washington,  D.  C.);  and  many  other  almanacs 
give  their  approximate  positions.  The  Publications  of  the  Astro- 
nomical  Society  of  the  Pacific  (address  819  Market  Street,  San  Fran- 
cisco), and  the  journal  Popular  Astronomy  (address  Northfield, 
Minnesota),  contain  such  information,  in  a  form  useful  to  amateurs. 
Lists  of  the  eclipses  of  each  year,  and  of  morning  and  evening  stars, 
are  printed  in  most  diaries,  as  well  as  the  phases  of  the  Moon,  and 
the  hours  of  sunrise  and  moon  rise,  etc.  The  daily  newspapers  fre- 
quently print  articles  naming  the  planets  and  stars  that  are  in  a  favor- 
able position  for  observation. 

Mercury  is  often  to  be  seen,  if  one  knows  just  where  to  look.  Its 
greatest  elongation  from  the  Sun  is  about  29°,  so  that  it  is  seldom  vis- 
ible in  our  latitudes  more  than  two  hours  afte  r  sunset,  or  before  sun 

414 


HINTS  ON  OBSERVING.  415 

rise.  The  student  will  do  well  to  know  its  place  (from  some  almanac) 
before  looking  for  it,  so  that  no  time  may  be  lost  in  discovering  this 
planet  over  agrun.  The  greatest  elongation  of  Venus  from  the  Sun 
is  about  45°,  so  that  this  planet  is  usually  not  visible  more  than  about 
three  hours  after  sunset,  or  before  sunrise.  In  a  clear  sky,  however, 
Venus  may  be  seen  in  the  daytime,  if  the  position  is  known.  Mars  is 
easy  to  distinguish  from  the  other  planets  by  his  ruddy  color.  Jupiter 
is  the  planet  next  in  brightness  to  Venus,  and  both  Jupiter  and  Venus 
are  brighter  than  the  most  brilliant  fixed  star — Sirius.  The  place  of 
Sirius  in  the  sky  can  be  found  on  any  one  of  the  star-maps,  and  hence 
Sirius  can  always  be  distinguished  from  the  planets.  Saturn  looks 
like  a  rather  dull  (not  sparkling)  fixed  star.  These  are  the  planets 
easily  visible  to  the  naked  eye.  If  the  student  finds  a  bright  object 
in  the  sky,  he  can  decide  from  the  star-maps  whether  it  is  a  fixed 
star.  If  it  is  not  a  star,  it  will  not  be  difficult  for  him  to  determine 
which  of  the  planets  he  has  found.  Uranus  is  occasionally  (just) 
visible  to  the  naked  eye,  but  Neptune  always  is  invisible,  except  in  a 
telescope.  At  least  one  of  the  asteroids  (  Vesta)  is  sometimes  visible 
to  the  naked  eye. 

The  motions  of  the  planets  may  be  studied  with  the  unaided  eye, 
but  nothing  can  be  known  of  their  disks  or  of  their  phases  without 
a  telescope.  An  opera-glass  (which  usually  magnifies  about  2  or  3 
times)  or,  better,  a  field-glass,  will  be  of  much  use  in  viewing  the 
Moon,  and  if  nothing  better  is  available  it  should  be  used  to  view  the 
planets.  But  even  a  small  telescope  is  much  more  satisfactory. 

The  student  must  not  expect  to  see  the  planetary  disks  as  they  are 
shown  in  the  drawings  of  this  book.  These  drawings  have  usually 
been  made  with  large  telescopes.  Even  under  very  favorable  condi- 
tions such  observations  are  more  or  less  disappointing  to  observers 
who  are  not  practised. 

Observations  of  Stars,  Nebulae,  Comets,  etc.— The  brighter  stars  can 
be  identified  in  the  sky  from  the  star-maps  in  this  book.  Some  of 
the  variable  stars  and  clusters  are  marked  in  Fig.  213.  Tables  V  to 
VIII  (pages  417  to  421)  give  the  places  of  some  of  the  principal 
fixed  stars,  doub'e-stars,  etc.  These  objects  (if  they  are  bright 
enough)  should  first  be  identified  with  the  naked  eye  and  then  studied 
with  the  best  telescope  available.  An  opera-glass  is  better  than 
nothing ;  a  good  field-glass  or  a  spy-glass  is  better  yet  (it  represents 
GALILEO'S  equipment),  but  a  telescope  of  several  inches  aperture 
with  a  magnifying  power  of  50  diameters  or  more,  on  a  firm  stand, 
should  be  used  if  it  is  possible  to  obtain  it. 

Photography  in  observation.— If  the  student  understands  photogra 


416  ASTRONOMY. 

phy  let  him  try  his  camera  on  the  heavens.  If  he  directs  it  to  the 
north  pole  and  gives  an  exposure  of  a  couple  of  hours  he  will  obtain 
the  trails  of  the  brighter  circumpolar  stars  (see  Fig.  29).  An  expo- 
sure of  a  few  minutes  on  a  bright  group  of  stars  near  the  zenith  or 
in  the  south  (the  Pleiades  or  Orion,  for  example)  will  give  trails  of  a 
different  kind  (see  Fig.  80).  In  both  these  observations  the  camera 
must  remain  fixed,  undisturbed  by  wind  or  jars  of  any  kind. 

If  he  can  strap  his  camera  to  the  tube  of  a  telescope  (like  that 
shown  in  Fig.  79)  he  can  follow  a  group  of  stars  in  their  motion 
from  rising  to  setting  by  using  the  telescope  as  a  finder  in  the  follow- 
ing way :  I.  Select  the  group  to  be  photographed.  It  should  be 
visible  in  the  camera  and  some  bright  star  of  the  group  should  be 
visible  in  the  telescope  at  the  same  time.  The  eyepiece  of  the  tele- 
scope should  be  provided  with  a  pair  of  cross  wires,  thus  -J-,  which 
the  observer  can  easily  insert,  if  necessary.  II.  The  image  of  one  of 
the  group  of  stars  must  be  kept  on  the  cross-wires  (by  gently  and 
constantly  moving  the  telescope  from  east  towards  west — from  rising 
toward  setting)  so  long  as  the  exposure  is  going  on.  In  this  way 
fairly  long  exposures  can  be  made.  If  the  image  of  the  guiding-star 
is  put  slightly  out  of  focus  the  guiding  is  sometimes  easier.  This 
method  is  also  available  for  photographing  a  bright  comet;  only  the 
student  must  remember  to  use  the  comet  itself  as  a  guiding-star  (in 
the  telescope),  because  the  comet  has  a  motion  among  the  stars. 
Photographs  of  the  Moon  (and  Sun)  can  be  made  with  small  cameras, 
but  unless  the  camera  has  a  long  focus  they  are  disappointingly 
small  in  size.  Let  the  student  try  to  make  them,  however.  For 
the  Moon,  use  the  quickest  plates.  For  the  Sun,  use  the  slowest 
plates,  the  smallest  stop  and  the  quickest  exposure.  In  these,  as  in 
all  observations,  the  important  matter  to  the  student  is  to  make  them 
and  to  find  out  what  is  wrong ;  and  then  to  make  them  over  again, 
correcting  mistakes  ;  and  so  on  until  a  satisfactory  result  is  obtained. 

It  is  desirable  that  the  school  should  own  apparatus  to  be  used  by 
the  students  under  the  direction  of  the  master.  A  short  list  follows : 
A  celestial  globe;  a  cheap  watch  regulated  to  sidereal  time;  a  straight- 
edge some  three  feet  long  ;  a  plumb-line ;  a  field-glass  ;  a  small 
telescope  ;  a  star-atlas  (UPTON'S,  MCCLURE'S  edition  of  KLEIN'S, 
PROCTOR'S,  are  good);  books  on  practical  Astronomy  (begin  with 
SERVISS'  Astronomy  with  an  Opera-Glass,  PROCTOR'S  Half  Hours  with 
the  Stars,  J.  WESTWOOD  OLIVER'S  Astronomy  for  Amateurs,  WEBB'S 
Celestial  Objects  for  Common  Telescopes,  and  add  to  these  as  needs 
arise);  books  on  descriptive  Astronomy  (begin  with  the  works  of  Sir 
ROBERT  BULL,  Miss  CLERKE'S  History  of  Astronomy  in  the  XIX 
Century,  FLAMMARION'S  Popular  Astronomy,  etc.,  and  add  to  these  as 


LIST  OF  BRIGHT  STARS. 


417 


opportunity  offers);   text-books  of  Astronomy  (begin  with  YOUNG'S 
General  Astronomy) . 

TABLE  V. 

MEAN  RIGHT  ASCENSION  AND  DECLINATION  OP  A  FEW  BRIGHT 
STARS,  VISIBLE  AT  WASHINGTON,  FOR  JANUARY  1,  1899. 


NAME  OF  STAR. 

Mag. 

Right 
Ascension. 

Annual 
Varia- 
tion. 

Declination. 

Annual 
Varia- 
tion. 

a    Andromedae 

2 

h.  m.    s. 
0     3     9.9 

s. 

4-  3  08 

4  28    31    58 

4-20  1 

a    Cassiopeiae  Far. 

2U 

0  34  46.3 

4-  3.37 

4  55    59      0 

4-19.8 

/3    Ceti        

Q'* 

0  38  31.2 

4-  3  00 

-  18    32    28 

4  19  8 

a    Ursae  Minoris  (Pole  Star).  .  . 
ft    Arietis  

2 
3 

1  22     8.0 
1   49     35 

4-24.99 
4-  3  30 

4-88    46      8 
-f  20    18    52 

418.8 
4  17  8 

a    Arietis       ... 

2 

2     1   28  7 

4-  3  36 

4  22    59      6 

4  17  3 

a    Ceti  

2U 

2  56  59  9 

4-  3  13 

4-    3    41     36 

4-  14  4 

a    Persei 

o'3 

3  17     65 

4-  4  26 

4  49    30      6 

4  13  1 

TJ    Tauri  

3 

3  41   28  7 

4-  3.56 

4-  23    47    34 

4-ll!4 

y1  Eridani..   . 

3 

3  53  18  9 

4-  2  79 

13    47    45 

4-  10  5 

a    Tauri  (Aldebaran).  ... 

1 

4  30     74 

4  3  43 

4-  16    18    23 

_i_    7.7 

t    Aurigae               .      ..  .  . 

4  50  24  9 

4-  3  90 

4-  33      0    23 

_j_    6  0 

a    Aurigae  (C'opellit) 

1 

5     9   13  5 

4  4  42 

4-  45    53    43 

4-44 

ft    Orionis  (Rigel)  
ft    Tauri  

1 
2 

5     9  41.0 
5   19  54  4 

4-  2.88 
4  3  79 

-    8    19      5 
4-  28    31    20 

+   4.4 
435 

S    Orionis 

214 

5  26  50  7 

4-  3  06 

0    22    26 

429 

5  28   16  5 

4-  2  65 

17    53    41 

L    2  8 

e    Orionis  

2 

5  31     53 

4-  3  04 

—    1     15    59 

4-25 

a    Columbae  

2U 

5  35  59  5 

4-  2.17 

-  34      7    40 

4-    2.1 

a    Orionis         .... 

1 

5  49  4'J  2 

4-  3  25 

4    7    23    18 

409 

y   Geminorum 

2 

6  31   52  6 

4-  3  46 

4-  16    29      8 

2  8 

a    Canis  Majoris  (Sirius)  .  .  .  , 

1 

6  40  41  9 

4  2  68 

-    16    34    41 

3  5 

e    Canis  Majoris         .... 

6  54  39  3 

4-  °  36 

28    50      4 

4  7 

a2  Geminorum  (Castor)  
a    Canis  Minoris  (Procyori)  .... 
ft    Geminorum  (Pollux)  
15  Argus  

2 
1 

1 
3 

7  28     9.4 
7  34     1.0 
7  39     8.2 
8     3  14  5 

4-  3.85 
4  3.19 
-f  3.73 
4-  2  56 

432      6    36 
4-    5    29      3 
+  28    16    12 
—  24      0    48 

-    7.5 

-    8.0 
-    8.4 
10  3 

i    Ursae  Majoris  

3 

8  52  17  7 

4-  4  17 

4  48    26    18 

13  7 

2 

9  22  37  4 

4  2  95 

8    13    15 

15  5 

9    Ursee  Majoris 

3 

9  26     63 

_i_  4  14 

_i_  52      g    75 

T>  7 

a    Leonis  (Regulus)  
y1  Leonis  ....        .... 

1 
21^ 

10     2  59.6 
10  14  24  3 

--  3.22 
4-  3  29 

+  12    27    39 
4  20    21      9 

-  17.5 
—  18  0 

a    Ursae  Majoris  

o'& 

10  57  29  8 

4  3  76 

_|_  62    17    46 

19  3 

ft    Leonis    

2 

11   43  54  5 

4  3  10 

-f-  15      8    12 

20  0 

y   Ursse  Majoris 

2L<; 

11   48  31  2 

4-  3  17 

-4-  *»4     TS    2^ 

20  0 

<r    Corvi  

** 

12     4  55  7 

4-  3  08 

22      3    30 

20  0 

ft   Corvi  

3 

12  29     48 

13  14 

22    50    18 

1Q  Q 

a    Canum  Venaticorum  
a    Virginis  (Spica)  

3 

1 

12  51    18.2 
13   19  52  2 

2.83 
3  16 

438    51    50 
10    38      3 

-  19.6 
18  8 

TJ    Ursae  Ma.  joris.  ... 

2 

13   43  33  7 

4-  2  38 

-4-  4Q    4Q      2 

18  0 

a    Bootis  (Arcturus)  
a    Librae  

1 
3 

14   11     3.2 
14  4R   17  3 

4-  2.81 
4  3  32 

+  19    42    30 

IK       07       OA 

-  16.9 

ft    Ursae  Minoris 

2 

14  50  59  7 

0  21 

+74     34       fi 

ft    Librae 

m/ 

15   11   34  2 

+     0    OO 

a    Coronae  Borealis  
a    Serpentis 

&k 

216 

15  30  24.6 
15  33  17  5 

4-  2.53 
4-  2  Q4 

+  27      3    16 

-  12.2 

ft1  Scorpii  

ft 

15  59  33  7 

4  3  48 

10  1 

3 

16  22  37  4 

+  0  81 

a    Scorpii  (Antares)  

1 

16  23   12  7 

I  •  3  67 

26     12     °S 

09 

a1  Herculis  
ft    Draconis  

I* 

17   10     2.5 
17  28     Q  0 

4  2.74 

i      i    of* 

4-14    30    19 

-    4.3 

418 


ASTRONOMY. 


TABLE    V.— Continued. 


NAME  OF  STAR. 

Mag. 

Right 
Ascension. 

Annual 
Varia- 
tion. 

Declination. 

Annual 
Varia- 
tion. 

3 

h.  m.    B. 

17  30  14  7 

s. 

4-  2  78 

0            1           II 

+  12    38      0 

// 
2  6 

Lyras  (Vega)            .  . 

1 

18  33  31  1 

-f  2.01 

4-  38    41     22 

+   29 

3i-4i 

18  4G  21  0 

_|_  2  21 

+  33    14    43 

+    40 

Aquilse  (Altair) 

1 

19  45  51  3 

_|_  2  89 

_|_    g    36      5 

+  s'o 

Cygni               .... 

20  37  59  3 

+  2  04 

+  44    55      9 

+  12  8 

Cephei  
Aquarii     

3 

21    16   10.1 
21    26   14  5 

+  1.41 
4-  3  16 

+  62      9    27 
—    6      0    56 

--15.1 
+  15.7 

Aquarii              .... 

3 

22     0  35  7 

+  3  08 

0    48    38 

+  17  4 

PiscisAustralis(FomaJ/ian<) 
Pegasi  (Markab)  

8| 

22  52     4.1 
22  59  43.7 

-f  3.30 

+  2  98 

-  30      9    27 

_|_  14    39    42 

--19.  2 

+  19  4 

4 

23  54     7.4 

+  3  07 

+    6    18    15 

+  20.0 

N.B. — The  Mean  Right  Ascension  and  Declination  for  any  other  year  than  1899 
may  be  found  from  this  table  by  multiplying  the  annual  variation  by  the  num- 
ber of  years  elapsed,  and  applying  the  result  to  the  quantities  given  in  this 
table.  If  the  required  date  be  earlier  than  1899,  the  signs  of  the  annual  varia- 
tions must  be  changed.  In  applying  such  corrections  to  the  Declinations  the 
corrections  must  be  added  algebraically.  For  example,  the  mean  place  of 
Aldebaran  for  July  1,  1901  (=  1901.5)  is  R.  A.  4h  30™  16".0  Decl.  +  16°  18'  42". 

N.B. — The  Nautical  Almanac  gives  the  apparent  R.A.'s  of  these  and  other 
stars  at  intervals  of  ten  days. 

N.B.— When  any  one  of  these  stars  is  on  the  observer's  meridian  at  any  date, 
his  local  sidereal  time  is  equal  to  that  star's  apparent  right  ascension  on  that 
date. 

The  foregoing  table  will  serve  to  set  the  observer's  watch  to  side- 
real time  within  a  few  minutes  so  soon  as  he  knows  his  meridian 
(see  page  151).  A  watch  set  approximately  to  sidereal  time  is,  of 
course,  necessary  in  identifying  objects  in  the  sky. 


LIST  OF  DOUBLE  STARS. 


419 


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420 


ASTRONOMY. 


TABLE  VII.     ;: 
A  LIST  OF  A  FEW  VARIABLE  STARS. 


STAR. 

R.  A. 

Decl. 

Period. 

Magnitude. 

Remarks. 

Max. 

Min. 

Mira  Ceti 

h          m 

2    14 
3      2 

4    55 

6    58 
9    42 

10    38 
13    24 
17    10 
.17    41 

18    46 

22    25 
23    53 

0               / 

-    3    26 
+  40    34 

+  43    41 

+  20    43 
+  11    54 
+  69    18 
-  22    46 
+  14    30 
-27    48 

+  33    15 

+  57    54 
+  50    50 

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331 

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305 
497 
90? 
7 

12.9 

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429 

1.7 
2.3 

3 

3.7 
5.2 
6 
3.5 
3.1 
4 

3.4 

3.7 
5 

uj 

3.5J 

4.5] 

4.5 
10 
13 
9.7 
3.9 
6 

4.5J 

... 

12 

It  is  best  seen  about 
October. 
Observe  it  in  Octo- 
ber &  November. 
Irregular.    Of  the 
Algol  type. 

Irregular  period. 
Observe  it  in  June. 
Observe  it  at  mid- 
summer. 
Observe  it  in  Aug. 
and  September. 

Algol  (/3  Persei). 
e   AurigcB 

$   Geminorum  .... 
R  Leonis  

R  Ursce   Majoris  .  . 
R  Hydrce  

X  Sagittarii  
/3   Lyrce  

&    Cephei  

R  Cassiopeia*  

LIST  OF  NEBULAS  AND   CLUSTERS. 


421 


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422 


ASTRONOMY. 


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HINTS  ON  OBSERVING.  423 

To  see  a  nebula  with  advantage  it  is  sometimes  advisable  to  set  the 
telescope  a  very  little  west  of  it  so  that  the  nebula  may  enter  the  field 
of  view  by  its  diurnal  motion  and  pass  slowly  across  it.  This  can  be 
repeated  as  often  as  desired.  Nearly  all  of  these  objects  are  so  faint 


FIG.  212. — MAP  OF  THE  STARS  (TO  FOURTH  MAGNITUDE  INCLU- 
SIVE) NEAR  THE   NORTH  CELESTIAL  POLE. 
The  names  of  these  stars  can  be  found  in  figures  214  to  219  following. 

that  no  artificial  lights  should  be  near  the  observer's  place.  The  word 
"bright"  in  the  descriptions  is  a  relative  term.  A  bright  nebula  is 
faint  compared  to  a  planet. 


424  ASTRONOMY. 


MAPS  OF  THE  STARS. 

The  Northern  Stars, — The  constellations  near  the  pole 
can  be  seen  on  any  clear  night,  while  most  of  the  southern 
ones  can  only  be  seen  during  certain  seasons,  or  at  certain 
hours  of  the  night.  Fig.  212  shows  all  the  stars  down  to 
the  fourth  magnitude,  inclusive,  within  50°  of  the  pole. 

The  Roman  numerals  around  the  margin  show  the 
meridians  of  right  ascension,  one  for  every  hour.  In  order 
to  have  the  map  represent  the  northern  constellations  as 
they  are,  it  must  be  held  so  that  the  hour  of  sidereal 
time  at  which  the  observer  is  looking  at  the  heavens  shall 
be  at  the  top  of  the  map.  The  names  of  the  months 
around  the  margin  of  the  map  show  the  regions  near  the 
zenith  during  those  months.  Suppose  the  observer  to 
look  at  nine  o'clock  (mean  solar  time)  in  the  evening,  to 
face  the  north,  and  to  hold  the  map  with  the  month  up- 
ward, he  will  have  the  northern  heavens  as  they  appear, 
except  that  the  stars  near  the  bottom  of  the  map  may  be 
cut  off  by  his  horizon. 

The  Equatorial  Stars. — The  folded  map,  Figure  213, 
shows  the  equatorial  stars  lying  between  30°  north  and  30° 
south  declination.  The  outlines  of  the  constellations  are 
indicated  by  dotted  lines.  The  figures  of  men  and  animals 
with  which  the  ancients  covered  the  sky  are  omitted. 
The  Latin  name  within  each  boundary  is  the  name  of  the 
constellation.  The  Greek  letters  serve  to  name  the  bright- 
est stars.  The  parallels  of  declination  (for  every  15°)  and 
the  hour-circles  (every  hour)  are  laid  down. 

The  magnitudes  of  the  stars  are  indicated  by  the  sizes  of 
the  dots.  To  use  this  map  it  must  be  remembered  that  as 
you  face  the  south  greater  right  ascensions  are  on  your  left 
hand,  less  on  your  right.  The  right  ascensions  of  the  stars 
immediately  to  the  south  between  6  and  7  P.M.  are: 


MAPS  OF  THE  STARS.  425 


For  January    1,    1  hour;       For  July  1,  13  hours; 


February  1,    3  hours; 
March       1,    5     " 
April        1,    7     " 
May          1,    9     " 
June          1,  11     " 


August  1,  15 
September  1,  17 
October  1,  19 
November  1,  21 
December  1,  23 


This  map  and  the  map  preceding  it  will  be  found  use- 
ful in  various  ways.  The  six  star-maps  that  follow  are 
more  convenient  for  ordinary  use,  however. 

Six  Star-maps  showing  the  Brighter  Stars  visihle  in  the 
Northern  Hemisphere.* — The  star-maps  in  this  series  were 
originally  adapted  to  a  north  latitude  of  about  52°,  so  that, 
for  the  latitudes  of  the  United  States,  they  will  be  slightly 
in  error,  but  not  so  much  as  to  cause  inconvenience.  Under 
each  map  will  be  found  the  date  and  time  at  which  the  sky 
will  be  as  represented  in  the  accompanying  map ;  e.  g. ,  Map 
No.  1  shows  the  sky  as  it  appears  on  November  22d  at  mid- 
night, December  5th  at  11  o'clock,  December  21st  at  10 
o'clock,  January  5th  at  9  o'clock,  and  January  20th  at  8 
o'clock. 

The  maps  are  intended  for  use  between  the  hours  of  8 
o'clock  in  the  evening  and  midnight,  and  the  titles  are 
given  with  reference  to  such  a  use. 

It  should  be  borne  in  mind,  however,  that  the  same  map  represents 
the  aspect  of  the  constellations  on  other  dates  than  those  given,  but 
at  a  different  hour  of  the  night.  Map  No.  I,  for  example,  shows  the 
aspect  of  the  sky  on  October  23d  at  2  A.  M.,  September  23d  at  4  A.  M., 
and  also  on  February  20th  at  6  P.  M.,  as  well  as  on  the  dates  and  at 
the  hours  given  in  the  map.  For  any  date  between  those  given,  the 
map  will  represent  the  sky  at  a  time  between  the  hours  given ;  for 
instance,  on  November  26th,  Map  No.  I  will  represent  the  sky  at 
11:45  o'clock,  on  November  30th  at  11:30  o'clock,  and  on  December  2d 
at  11:15  o'clock. 

If  the  maps  are  held  with  the  centre  overhead  and  the 
top  pointing  to  the  north,  the  lower  part  of  the  map  will  be 

*  From  the  publications  of  the  Astronomical  Society  of  the  Pacific, 
1898. 


426 


ASTRONOMY. 


to  the  south,  the  right-hand  portion  will  be  to  the  west,  and 
the  left-hand  to  the  east,  and  the  circle  bounding  the  map 
will  represent  the  horizon.  Each  map  is  intended  to  show 
the  whole  of  the  sky  visible  at  these  times. 

The  names  of  the  constellations  are  inserted  in  capitals, 
while  the  names  of  stars  and  other  data  are  in  small  letters. 

Constellations  on  the  meridian  about  midnight : 

January :       Camelopardus,  Lynx,  Gemini,  Monoceros,  Orion,  Canu 

major. 

February  :     Ursa  major,  Lynx,  Cancer,  Hydra. 
March  :          Ursa  major,  Leo,  Hydra. 
April:  Bootes,  Libra. 

May:  Hercules,  Ophiuchus,  Scorpio. 

June:  Lyra,  Hercules,  Sagittarius. 

July:  Cygnus,  Aquila,  Sagittarius. 

August:        Cepheus,  Cygnus,  Capricornus. 
September:  Cepheus,  Pegasus,  Aquarius. 
October:        Cassiopeia,  Andromeda,  Pisces. 
November:   Perseus,  Aries,  Cetus. 
December:     Camelopardus,  Taurus,  Orion 


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*th  and  30   Soutli  Declination, 


(Henry  J£olt  <*  OojXjaa  York) 


MAPS  OF  THE  STARS. 


427 


MAPI. 
North. 


-•I 


South. 

FIG.  214. 

The  sky  on  November  23,  at  12  o'clock  P.M. 
December  6,  at  11  o'clock  P.M. 
December  21,  at  10  o'clock  P.M. 
January  5,  at  9  o'clock  P.M. 
January  20,  at  8  o'clock  P.M. 


428 


ASTRONOMY. 


MAPIL 

North. 


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FIG.  215. 

The  sky  on  January  20,  at  12  o'clock  P.M. 
February  4,  at  11  o'clock  p  M. 
February  19,  at  10  o'clock  P.M. 
March  6,  at  9  o'clock  P.M. 
March  21,  at  8  o'clock  P.M. 


MAPS  OF  THE  STABS. 


429 


MAP  III. 

North, 


South. 

FIG.  216. 

The  sky  on  March  21,  at  12  o'clock  P.M. 
April  5,  at  11  o'clock  P.M. 
A_pril  20,  at  10  o'clock  P.M. 
May  5,  at  9  o'clock  P.M. 
May  21,  at  8  o'clock  P.M. 


430 


ASTRONOMY. 


MAP  IV. 

North. 


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South. 

FIG.  217. 

The  sky  on  May  21,  at  12  o'clock  P.M. 
June  5,  at  11  o'clock  P.M. 
June  21,  at  10  o'clock  P.M. 
July  7,  at  9  o'clock  P.M. 
July  22,  at  8  o'clock  P.M. 


MAPS  OF  THE  STARS. 


431 


MAP  V. 

North. 


South. 

FIG.  218. 

The  sky  on  July  22,  at  12  o'clock  P.M. 

August  7,  at  11  o'clock  p  M. 
August  23,  at  10  o'clock  P.M. 
September  8,  at  9  o'clock  P.M. 
September  23,  at  8  o'clock  P.M. 


432 


ASTRONOMY. 


MAP  VI. 

North. 


LV> 


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*>** 


X 


South. 

FIG.  219. 

The  sky  on  September  23,  at  12  o'clock  P.M. 
October  8,  at  11  o'clock  P.M. 
October  23,  at  10  o'clock  P  M. 
November  7,  at  9  o'clock  P.M. 
November  22,  at  8  o'clock  P.M. 


APPENDIX. 

SPECTRUM   ANALYSIS. 

ALTHOUGH  the  subject  of  Spectrum  Analysis  belongs 
properly  to  physics,  a  brief  account  of  its  relations  to 
astronomy  may  be  useful  here. 

To  understand  the  instruments  and  methods  of  Spectrum 
Analysis  it  will  be  necessary  to  recall  the  optical  properties 
of  a  prism,  which  are  demonstrated  in  all  treatises  on  phys- 
ics. 

The  Prism. — When  parallel  rays  of  homogeneous  light,  red  for  ex- 
ample, fall  on  a  face  of  a  prism  they  are  bent  out  of  their  course,  and 
when  they  emerge  from  the  prism  they  are  again  bent,  but  they  still 
remain  parallel;  thus  the  rays  rr,  r"  ?•",  are  bent  into  the  final  di- 
rection r'  r'.  This  is  true  for  parallel  rays  of  every  color.  They  re- 
main parallel  after  deviation  by  the  prism.  This  can  be  shown  by 
experiment.  If  the  incident  rays  r  r,  in  Fig.  220,  are  red,  they  will 
come  to  the  screen  at  r'  r'.  If  they  are  violet  rays,  they  will  come  to 
vf  v'  on  the  screen,  after  having  been  bent  more  from  their  original 
course  than  the  red  rays.  The  violet  rays,  with  the  shortest  wave- 
length, are  the  most  refrangible.  The  red,  with  the  longest  wave- 
length, are  the  least  refrangible. 

The  experiments  of  Sir  ISAAC  NEWTON  (1704)  proved 
the,!;  white  light  (as  sunlight,  moonlight,  starlight)  was  not 
simple,  but  compound.  That  is,  white  light  is  made  up  of 
light  of  different  wave-lengths.  Difference  of  wave-length 
shows  itself  to  the  eye  as  difference  of  color.  Seven  colors 
were  distinguished  by  NEWTON;  viz.,  violet,  indigo,  blue, 
green,  yellow,  orange,  red.  (Memorize  these  in  order.  It 
is  the  order  of  the  colors  in  the  rainbow.)  If  parallel  rays 
of  white  light,  as  sunlight,  r  r,  fall  on  a  prism,  the  red  rays 

433 


434  APPENDIX. 

of  this  beam  will  still  fall  at  r'  r',  and  the  violet  rays  will 
fall  at  v  v'.  Between  v'  and  r'  the  other  rays  will  fall,  in 
the  order  just  given;  that  is,  in  the  order  of  their  refrangi- 
bility.  The  rainbow-colored  streak  on  the  screen  is  called 
the  spectrum;  it  is  a  solar,  a  lunar,  or  a  stellar  spectrum 
according  as  the  source  of  the  rays  is  the  Sun,  Moon,  or  a 


FIG.  220.— THE  ACTION  OP  A  PRISM  ON  A  BEAM  OF  WHITE  LIGHT. 

star.  The  solar  spectrum  is  very  bright;  the  lunar  spec- 
trum is  much  fainter;  and  the  spectrum  of  a  star  is  far 
fainter  than  either. 

If  we  let  parallel  rays,  r  r,  of  red  light  come  through  a  circular 
hole  at  Q  (Fig.  220),  they  will  form  a  circular  image  of  the  hole  at 
r'  r'.  If  the  hole  is  square  or  triangular,  a  square  or  a  triangular 
image  will  be  formed.  If  it  is  a  narrow  slit,  a  narrow  streak  of  red 
light  will  be  projected  at  r'  r'. 

When  wJiite  light  is  passed  through  a  circular  hole  at  Q,  circular 
images  of  the  hole  are  formed  all  along  the  line  r'  rf  to  v'  v' :  the  red 
images  at  r'  r',  the  orange,  yellow,  green,  blue  images  in  succession, 
and  the  violet  image  at  v'  v'.  If  the  hole  is  of  any  size  these  images 
will  overlap,  so  that  the  colors  are  not  pure.  If  white  light  falls 


SPECTRUM  ANALYSIS.  435 

through  a  narrow  slit  at  Q,  placed  parallel  to  the  edge  A  of  the 
prism,  the  purest  spectrum  is  obtained.  The  different  spectra  do  not 
overlap. 

FRAUNHOFER  tried  this  experiment  in  1804,  and  he 
found  that  the  spectrum  of  the  Sun  was  interrupted  by  cer- 
tain dark  lines,  fixed  in  relative  position.  These  are  the 
Fraunhofer  lines, -so  called.  He  made  a  map  of  the  solar 
spectrum,  and  on  the  map  he  placed  the  various  lines  in 
their  proper  places.  These  lines  appear  in  the  same  rela- 
tive position  no  matter  whether  a  slit  or  a  very  small  cir- 


FIG.  221. — THE  SPECTROSCOPE. 

cular  hole  is  used,  and  they  belong  to  the  incident  light 
and  are  not  produced  by  the  apparatus.  This  simply  ren- 
ders them  visible.  They  are  not  seen  when  the  light  comes 
through  wide  apertures,  on  account  of  the  overlapping  of 
the  various  images.  (See  Fig.  222.) 

The  Spectroscope. — A  spectroscope  consists  essentially  of 
one  or  more  prisms  (or  any  other  device,  as  a  diffraction 
grating)  by  means  of  which  a  spectrum  is  produced;  of  a 
means  to  make  the  spectrum  pure  (a  slit  and  collimator), 
and  of  a  means  to  see  it  well  (a  small  telescope). 


436  APPENDIX. 

Fig.  221  shows  the  arrangement  of  a  one-prism  spectro- 
scope. The  light  enters  the  slit  S,  which  is  exactly  in  the 
focus  of  the  objective  A  of  the  collimator.  The  rays  there- 
fore emerge  from  A  in  parallel  lines.  They  are  deviated 
by  the  prism  P,  and  enter  the  objective  B,  forming  an 
image  of  the  spectrum  at  0,  which  is  viewed  by  the  eye 
at  E. 

The  Solar  Spectrum. — Part  of  this  image  (of  the  solar 
spectrum)  is  shown  in  Fig.  222,  except  as  to  color.  The 


A    a     B     C  D  Eb  F 

FIG.  222.— A  PART  OF  THE  SOLAR  SPECTRUM. 

various  colors  extend  in  succession  from  end  to  end  of  the 
spectrum.  In  each  color  are  certain  dark  lines  which  have 
a  definite  position.  The  most  conspicuous  of  these  lines 
are  called  the  Fraunhofer  lines,  and  are  lettered  A,  B,  (7, 
Z),  E)  F,  G,  H.  A  is  below  the  easily  visible  red,  B  is  at 
its  lower  edge,  C  is  near  the  middle  of  the  red,  D  is  a  double 
line  in  the  orange,  J^is  in  the  green,  Fis  in  the  blue,  G  in  the 
indigo,  and  H  in  the  violet.  There  are  at  least  500  lines 
besides  which  can  be  seen  with  spectroscopes  of  moderate 
power.  Each  and  every  one  of  these  has  a  definite  position. 

When  the  instrument  drawn  in  Fig.  221  is  pointed  toward  the  Sun 
(so  that  the  Sun's  rays  fall  on  8),  the  spectrum  seen  is  that  of  the 
whole  Sun.  If  we  wish  to  examine  the  spectrum  of  a  part  of  the 
Sun,  as  of  a  spot  for  example,  we  must  attach  the  whole  instrument 
to  a  telescope,  so  that  8  is  in  the  principal  focal  plane  of  the  tel- 
escope-objective. An  image  of  the  Sun  will  then  be  formed  by 


SPECTRUM  ANALYSIS.  43? 

the  telescope-objective  on  the  slit  plate  8,  and  the  light  from  any 
part  of  that  image  can  be  examined  at  will.  The  spectroscope  is  also 
used  in  order  to  examine  stars.  We  employ  a  telescope  in  this  case 
so  that  its  objective  may  collect  more  light  and  present  it  at  the  slit 
of  the  spectroscope. 

Spectra  of  Solids  and  Gases. — A  solid  body,  heated  so 
intensely  as  to  give  ^J^QJifJ^^..^"~'GontimiOtiB  spectrum. 
That  is,  there  are  no  Fraunhofer  lines  in  it,  but  prismatic 
colors  only.  A  gaseous  body,  heated  so  intensely  as  to  give 
off  light,  has  a  discontinuous  spectrum.*  That  is,  the 
colors  red  to  violet  are  no  longer  seen,  but  on  a  dark  back- 
ground the  spectrum  shows  one  or  more  bright  lines. 

These  lines  have  a  definite  relative  position  and  are  char- 
acteristic of  the  particular  gas.  The  vapor  of  sodium,  for 
example,  gives  two  bright  lines,  whose  relative  position  is 
always  the  same,  as  laboratory  experiments  show. 

If  the  source  of  light  is  a  solid  body,  intensely  heated, 
the  spectroscope  will  show  a  continuous  spectrum  without 
lines,  as  has  been  said.  If  between  the  solid  body  and  the 
slit  of  the  spectroscope  we  place  a  glass  vessel  containing 
the  vapor  of  sodium,  the  spectrum  will  no  longer  be  without 
lines.  Two  dark  lines  will  appear  in  the  orange.  If  we 
remove  the  vapor  of  sodium,  the  lines  will  go  also.  They 
are  produced  by  the  absorptive  action  of  this  vapor  on  the 
incident  light. 

If  we  register  exactly  the  spot  in  the  field  of  view  of  the 
spectroscope  where  each  of  these  dark  lines  appears,  and  if 
we  then  remove  the  sodium  vapor  and  replace  the  solid 
body  (the  source  of  light)  by  intensely  heated  sodium  vapor, 
we  shall  find  the  new  spectrum  to  be  composed  of  two 
bright  lines,  as  has  been  said  ;  and  these  two  bright  lines 
will  occupy  exactly  the  same  places  in  the  field  of  view  that 
the  two  dark  lines  formerly  occupied. 

*  Unless  under  great  pressure,  when  the  spectrum  is  continuous,  as 
in  the  case  of  our  Sun,  and  of  stars  of  similar  constitution  to  the  Sun. 


438  APPENDIX. 

The  two  dark  lines  are  a  sign  of  the  kind  of  light  that  is 
absorbed  by  sodium  vapor  ;  the  two  bright  lines  are  a  sign 
of  the  kind  of  light  that  is  emitted  by  sodium  vapor.  These 
two  kinds  are  the  same.  What  is  true  of  sodium  vapor  is 
true  or  every  gas.  Every  gas  absorbs  light  of  the  same  kind 
(wave  length)  as  that  which  it  emits. 

If  a  spectroscopist  had  to  determine  what  kind  of  gas  was  contained 
in  a  certain  jar,  he  might  do  it  in  two  ways.  He  might  heat  it  in- 
tensely, and  measure  the  positions  of  the  bright  lines  of  its  spectrum; 
or  he  might  place  the  gas  between  the  slit  of  his  spectroscope  and  a 
highly  heated  solid  body,  and  measure  the  positions  of  the  dark  lines 
of  its  absorption-spectrum.  The  positions  of  the  lines  will  be  the 
same  in  both  cases.  By  comparing  the  measures  with  previous  meas- 
ures for  known  gases,  the  name  of  the  particular  gas  in  question 
would  become  known  to  him.  New  chemical  elements  have  been 
discovered  by  the  spectroscope.  The  spectrum  of  the  mixture  that 
contained  them  showed  previously  unknown  spectrum  lines.  They 
were  first  detected  by  the  presence  of  these  unknown  lines  and  then 
separated  from  the  known  gases  present  in  the  mixture. 

Comparison  of  the  Spectra  of  Incandescent  Gases  with 
the  Solar  Spectrum, — Laboratory  experiments  on  known 
gases  show  the  positions  of  the  spectral  lines  characteristic 
of  each  gas  or  vapor.  The  positions  of  the  lines  of  magne- 
sium or  of  hydrogen,  for  example,  are  accurately  known. 
The  positions  of  the  dark  lines  in  the  solar  spectrum  are 
also  known  with  accuracy.  It  is  found  that  nearly  every  one 
of  the  thousands  of  dark  lines  of  the  solar  spectrum  has  a 
position  corresponding  exactly  to  that  of  some  one  of  the 
lines  of  some  known  gas  or  of  the  vapor  of  some  known 
metal.  For  example,  the  vapor  of  iron  has  several  hundred 
lines,  whose  positions  are  accurately  known  by  laboratory 
experiments.  In  the  solar  spectrum  there  are  several 
hundred  whose  positions  precisely  correspond  to  the  lines 
of  iron  vapor.  The  same  is  true  of  many  other  substances, 
hydrogen,  sodium,  potassium,  magnesium,  nickel,  copper, 
etc.,  etc. 


SPECTR  UM  ANAL  7 SIS.  439 

From  this  it  is  inferred  that  the  Sun's  atmosphere  con- 
tains the  metal  iron  in  an  incandescent  state,  as  well  as  the 
vapors  of  the  other  substances  named. 

Let  us  see  the  process  of  reasoning  which  led  KOCHHOFF  and 
BUNSEN  (1859)  to  this  interpretation  of  the  observation. 

We  have  seen  (Part  II.,  Chap.  XVI)  that  the  Sun  is  composed  of  a 
luminous  surface,  the  photosphere,  surrounded  by  a  gaseous  envelope. 
The  photosphere  alone  would  give  a  continuous  spectrum  (with  no 
dark  lines).  The  gaseous  envelope  will  absorb  the  kind  of  light  that 
it  would  itself  emit.  The  absorption  is  characteristic.  If  a  solid  in- 
candescent body  were  placed  in  a  laboratory  and  surrounded  by  the 
vapors  of  iron,  hydrogen,  sodium,  etc.,  we  should  see  the  same  spec- 
trum that  we  do  see  when  we  examine  the  Sun. 

The  kind  of  evidence  is  easily  understood  from  the  foregoing.  Only 
the  spectroscopist  can  fully  appreciate  the  force  of  it.  The  resulting 
inference  that  the  Sun's  atmosphere  contains  the  vapors  of  the  metals 
named  is  certain.  These  vapors  exist  uncombined  in  the  Sun's  atmos- 
phere. The  temperature  and  the  pressure  are  too  high  to  allow  their 
chemical  combination. 


INDEX. 


Aberration  of  light,  257. 
Achromatic  telescope   described, 

121. 
ADAMS'S  work   on  perturbations 

of  Uranus,  342. 
Algol  (variable  star),  388. 
Altitude  of  a  star  defined,  81. 
ANAXIMANDER,  (B.  c.  610),  6. 
ANAXAGORAS  (B.  c.  500),  6. 
Angles,  22. 

Annular  eclipses  of  the  Sun,  230. 
Apex  of  solar  motion,  381. 
Apparent  motion  of  the  Sun,  154. 
Apparent  motion  of  a  planet,  180. 
Apparent  time,  90. 
ARCHIMEDES,  (B.  c.  287),  7. 
ARISTOTLE,  (B.  c.  384),  7. 
Asteroids,  322. 
Astronomical      instruments     (in 

general),  112. 
Astronomy  (defined),  1. 
Atmosphere  of  the  Moon,  317. 
Atmospheres  of  the  planets.    See 

Mercury,  Venus,  etc. 
Azimuth  denned,  81. 
BARNARD  discovers  satellite  of 

Jupiter,  325. 
BESSEL'S  parallax  of  61   Cygni 

(1837),  383. 
Binary  stars,  391. 


BOND'S  discovery  of  the  dusky 

ring  of  Saturn,  1850,  336. 
Books  (a  list  of),  416. 
BOUVARD  on  Uranus,  341. 
BRADLEY  discovers  aberration  in 

1729  256. 
BUNSEN,  439. 
Calendar,  247. 
CASSINI  discovers  four  satellites 

of  Saturn  (1684-1671),  339. 
Catalogues  of  stars,  376. 
Celestial  globe,  74. 
Celestial  photography,  145,  415. 
Celestial  sphere,  18. 
Centre   of  gravity   of  the  solar 

system,  275. 
Change  of  the  Day,  101. 
Chronology,  247. 
Chronometers,  115.     . 
Clocks,  112. 
Clusters  of  stars,  393. 
Comets,  357. 
Comets'  orbits,  361. 
Comets'    tails,     repulsive    force, 

363. 
Conjunction  (of  a  planet  with  the 

Sun)  defined,  183. 
Constellations,  371. 
Construction  of  the  heavens,  369. 
Co-ordinates  of  a  star,  77. 
441 


442 


INDEX. 


COPERNICUS,  8,  191. 

Cosmogony,  407. 

Corona  of  the  Sun,  282,  290. 

Dark  stars,  389. 

Day,  how  subdivided  into  hours, 

etc.,  83. 

Days,  mean  solar  and  solar,  90. 
Declination  of  a  star  defined,  30. 
Distance  of  the  fixed  stars,  381. 
Distribution  of  the  stars,  371. 
Diurnal  motion,  41,  59. 
DON  ATI'S  comet  (1858),  358. 
Double     (and    multiple)    stars, 

390. 

Earth,  general  account  of,  232. 
Earth's  density,  238. 
Earth's  dimensions,  234. 
Earth's  mass,  237. 
Eclipses  of  the  Moon,  224. 
Eclipses  of  Sun  and  Moon,  222. 
Eclipses  of  the  Sun,  explanation, 

228. 
Eclipses    of    the    Sun,    physical 

phenomena,  289. 
Eclipses,  their  recurrence,  230. 
Ecliptic  defined,  161. 
Elements   of    the   orbits   of    the 

major  planets,  276. 
Elongation  (of  a  planet),  183. 
ENCKE'S  comet,  367. 
Epicycles,  190. 
Equation  of  time,  150. 
Equator  (celestial)  defined,  30. 
Equatorial  telescope,  133. 
Equinoxes,  160,  163. 
ERATOSTHENES,  (B.  c.  276),  7. 
Eyepieces  of  telescopes,  121. 
FABRITIUS  observes  solar  spots 

(1611),  285. 
Figure  of  the  Earth,  232. 


FRAUENHOFER'S      Experiments 

with  the  Prism,  435. 
Future  of  the  solar  system,  413. 
Galaxy  or  milky  way,  372. 
GALILEO  invents   the    telescope 

(1609),  117. 
GALILEO    observes    solar    spots 

(1611),  285. 
GALILEO'S  discovery  of  satellites 

of  Jupiter  (1610),  325. 
GALLE  observes  Neptune  (1846). 

343. 
Gases,   spectra   of   incandescent, 

437;  in  meteoric  stones,  362. 
Geodetic  surveys,  235. 
Globe  (celestial),  74. 
Gravitation  extends  to  stars,  392. 
Gravitation  resides  in  each  par- 
ticle of  matter,  209. 
Gravity,  terrestrial,  204,  237. 
Gregorian  calendar,  247. 
HALLEY  predicts  the  return  of  a 

comet  (1682),  363. 
HALL'S  discovery  of  satellites  of 

Mars,  313. 
HERSCHEL  (W.)    discovers    two 

satellites  of  Saturn  (1789),  339. 
HERSCHEL  (W.)    discovers    two 

satellites  of  Uranus  (1787),  340. 
HERSCHEL  ( W. )  discovers  Uranus 

(1781),  339. 

HERSCHEL'S  catalogues  of  nebu- 
la?, 393. 
HERSCHEL  (W.)  states  that  the 

solar  system  is  in  motion  (1783), 

381. 
HERSCHEL'S  (W.)  views  on  the 

nature  of  nebulae,  395. 
Hints  on  observing,  414. 
HIPPARCHUS  (B.  c.  160),  7. 


INDEX. 


443 


Horizon  (celestial — sensible)  of 
an  observer  defined,  30,  31. 

Hour-angle  of  a  star  defined,  78. 

HUGGINS  first  observes  the  spec- 
tra of  nebulae  (1864),  397. 

HUYGHENS  discovers  a  satellite 
of  Saturn  (1655),  339. 

HUYGHENS'  explanation  of  the 
appearances  of  Saturn's  rings 
(1655),  334. 

Inferior  planets  defined,  185. 

JANSSEN  first  observes  solar 
prominences  in  daylight,  291. 

Julian  year,  247. 

Jupiter,  325. 

KANT'S  nebular  hypothesis,  408. 

KEPLER'S  laws  enunciated,  198. 

KIRCHHOFF,  439. 

LAPLACE'S  nebular  hypothesis, 
408. 

LAPLACE'S  investigation  of  the 
constitution  of  Saturn's  rings, 
338. 

LASSELL  discovers  Neptune's  sat- 
ellite (1847),  345. 

LASSELL  discovers  two  satellites 
of  Uranus  (1847),  340. 

Latitude  of  a  place  on  the  earth 
defined,  26,  59. 

Latitude  of  a  point  on  the  earth 
is  measured  by  the  elevation  of 
the  pole,  59. 

Latitudes  and  longitudes  (celes- 
tial) defined,  164. 

Latitudes  (terrestrial),  how  deter- 
mined, 105. 

LE  VERRIER  computes  the  orbit 
of  meteoric  shower,  355. 

LE  VERRIER'S  work  on  perturba- 
tions of  Uranus,  342. 


Light-gathering  power  of  an  ob- 
ject-glass, 122. 

Light-ratio  (of  stars)  is  about  ^, 
374. 

List  of  bright  stars,  417. 

List  of  double  stars,  419. 

List  of  variable  stars,  420. 

List  of  nebulae  and  clusters,  421. 

Local  time,  95. 

Longitude  of  a  place,  26,  96. 

Longitude  of  a  place  on  the 
earth  (how  determined),  98. 

Longitudes  (celestial)defined,  164. 

Lucid  stars  defined,  374. 

Lunar  phases,  nodes,  etc.  See 
Moon's  phases,  nodes,  etc. 

Magnifying  power  of  an  eye- 
piece, 120. 

Major  planets  defined,  270. 

Maps  of  the  stars,  423  et  seq. 

Mars,  303. 

Mars's  satellites  discovered  by 
HALL  (1877),  313. 

Mass  of  the  Sun  in  relation  to 
masses  of  planets,  265. 

Masses  of  the  stars,  378. 

Mean  solar  time  defined,  90. 

Mercury,  299. 

Meridian  (celestial)  defined,  34. 

Meridian  circle,  129. 

Meridian  line  (established),  152. 

Meridian  (terrestrial)  defined,  34. 

Meteoric  showers,  351. 

Meteoric  stones,  gases  in,  362. 

Meteors  and  comets,  their  rela- 
tion, 354. 

Meteors,  347. 

Micrometer,  141. 

Milky  Way,  372. 

Minor  planets  defined,  270. 


444 


INDEX. 


Minor  planets,  general  account, 

322. 

Mira  Ceti  (variable  star),  386. 
Model  of  a  meridian  circle,  132. 
Model  of  an  equatorial,  138. 
Months,  different  kinds,  246. 
Moon,  general  account,  315. 
Moon's  light  ti^nro  of  Sun's,  317. 
Moon's  phases,  216. 
Moon's  parallax,  262. 
Moon  photographs,  320. 
Moon,  spectrum  of  the,  317. 
Moon's  surface,  does  it  change  ? 

320. 
Motion  of  solar  system  in  space, 

404. 
Motion   of  stars  in   the  line  of 

sight,  401. 

Nadir  of  an  observer  defined,  30. 
Nautical  almanac  described,  150. 
Nebulae  and  clusters  in  general, 

393. 

Nebular  hypothesis  stated,  407. 
Neptune,    discovery    of,    by  LE 

VERRIER  and  ADAMS   (1846), 

341. 

Neptune,  341. 
New  stars,  387. 

NEWTON  (H.  A.)  on  meteors,  355. 
NEWTON  (I.),  The  Principia 

(1687),  8;   calculates  orbit  of 

comet  of  1680,  361  ;  Spectrum 

Analysis  experiments,  433, 
Objectives,  or  object-glasses,  120. 
Obliquity  of  the  ecliptic,  171. 
Occultations  of  stars  by  the  Moon 

(or  planets),  230. 
OLBERS'S  hypothesis  of  the  origin 

of  asteroids,  323. 
Old  style  (in  dates),  247. 


Opposition  (of  a  planet  to  the 
Sun)  defined,  183. 

Parallax  (in  general)  defined,  107. 

Parallax  of  the  Sun,  262. 

Parallax  of  the  stars,  general  ac- 
count, 109. 

Pendulum,  115. 

Periodic  comets,  363. 

Penumbra  of  the  Earth's  or 
Moon's  shadow,  131. 

Perturbations,  213. 

Photography — its  use  in  astron- 
omy, 145. 

Photographic  star- charts,  323. 

Photosphere  of  the  Sun,  281. 

PIAZZI  discovers  the  first  asteroid 
(1801),  323. 

Planets,  their  relative  size  ex- 
hibited, 277. 

Planetary  nebulae  defined,  397. 

Planets,  their  apparent  and  real 
motions,  179. 

Planets,  their  physical  constitu- 
tion, 345. 

Pole  of  the  celestial  sphere  de- 
fined, 46. 

Precession  of  the  equinoxes,  248. 

Prism,  The,  434. 

Problem  of  three  bodies,  213. 

Progressive  motion  of  light,  254, 
331. 

Proper  motion  of  the  sun,  379. 

Proper  motions  of  stars,  379. 

PTOLEMY  (B.  c.  140),  7,  190. 

PTOLEMY'S  system  of  the  world, 
190. 

PYTHAGORAS  (B.  c.  582),  6. 

Radiant  point  of  meteors,  352. 

Radius  vector,  195. 

Reflecting  telescopes,  123. 


INDEX. 


445 


Refracting  telescopes,  119. 

Refraction  of  light  in  the  atmos- 
phere, 242. 

Resisting  medium  in  space,  367. 

Reticle  of  a  transit  instrument, 
126. 

Retrogradations  of  the  planets 
explained,  187. 

Right  ascension  of  a  star  defined, 
30,  80. 

Right  ascensions  of  stars,  how 
determined  by  observation,  127. 

ROEMER  discovers  (1675)  that 
light  moves  progressively,  254. 

Saturn,  331. 

Seasons,  The,  174 

Sextant,  146. 

Sidereal  time  explained,  83. 

Sidereal  year,  246. 

Signs  of  the  Zodiac,  169. 

Solar  corona,  etc.     See  Sun. 

Solar  heat,  its  amount,  293. 

Solar  motion  in  space,  404. 

Solar  parallax,  262. 

Solar  prominences  gaseous,  291. 

Solar  system,  description,  269. 

Solar  system,  its  future,  413. 

Solar  temperature,  294. 

Solar  time,  90. 

Solstices,  162,  163. 

Space,  15. 

Spectroscope,  The,  435. 

Spectrum  Analysis,  433. 

Spectrum ;  Solar  corona,  291  ; 
Lunar,  317  ;  Nebulae  and  Clus- 
ters, 398;  Fixed  Stars,  400 ;  as 
indicating  motions  of  stars,  401 ; 
Solids  and  Gases,  437;  Solar, 
436. 

Standard  time  (U.  S.),  99. 


Star-clusters,  397. 

Stars — had  special  names    3000 

B.    c.,  375;  magnitudes,  374; 

parallax  and  distance,  381,  382; 

about  2000  seen  by  the  naked 

eye,  371;  proper  motions,  379; 

spectra,  400. 
Star-maps,  423  et  seq. 
STRUVE  (W!)  determines  stellar 

parallax  (1838),  383. 
Summer  solstice,  162. 
Sun's  apparent  path,  159. 
Sun's  atmosphere,  281,  289. 
Sun's  constitution,  280. 
Sun-dial,  114. 
Sun's  (the)  existence  cannot  be 

indefinitely  long,  413. 
Sun's  mass  over  700  times  that 

of  the  planets,  275. 
Sun,  physical  description,  280. 
Sun's  proper  motion,  404. 
Sun's  rotation-time  about  25  days, 

286. 
Sun,    Spectroscopic  observations 

of  the,  436. 

Sun-spots  and  faculae,  285. 
Sun-spots  are  confined  to  certain 

parts  of  the  disk,  286. 
Sun-spots,        their      periodicity, 

287. 

Superior  planets  (defined),  185 
SWEDENBORG'S  nebular  hypothe- 
sis, 408. 

Telescopes,  119. 
Telescopes  (reflecting),  123. 
Telescopes  (refracting),  119. 
TEMPEL'S  comet,  its  relation  to 

November  meteors,  354. 
Temporary  stars,  386. 
THALES  (B.  c.  640),  5. 


446 


INDEX. 


Tides,  219. 

Time,  83,  94. 

Total  solar  eclipses,   description 

of,  289. 

Trails  (of  stars),  51,  52. 
Transit  instrument,  124. 
Transits  of  Mercury  and  Venus, 

303. 

Transits  of  Venus,  264. 
Triangulation,  235. 
Twilight,  243. 
TYCHO  BRAHE  observes  new  star 

of  1572,  387. 
Units    of    mass    and     distance, 


Universal  gravitation  discovered 

by  NEWTON,  214. 
Uranus,  339. 
Variable    and    temporary    stars, 

386. 

Variable  stars,  theories  of,  387. 
Velocity  of  light,  255. 
Venus,  300. 
Vernal  equinox,  160. 
Weight  of  a  body  defined,  237. 
Winter  solstice,  163. 
Years,  different  kinds,  246. 
Zenith  defined,  30. 
Zodiac,  169. 
Zodiacal  light,  356. 


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University  of  California 

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